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Título : Classical Finite Transformation Semigroups : An Introduction Tipo de documento: documento electrónico Autores: Ganyushkin, Olexandr ; SpringerLink (Online service) ; Mazorchuk, Volodymyr Editorial: London : Springer London Fecha de publicación: 2009 Otro editor: Imprint: Springer Colección: Algebra and Applications, ISSN 1572-5553 num. 9 Il.: online resource ISBN/ISSN/DL: 978-1-84800-281-4 Idioma : Inglés (eng) Palabras clave: Mathematics Group theory Combinatorics Theory and Generalizations Clasificación: 51 Matemáticas Resumen: The aim of this monograph is to give a self-contained introduction to the modern theory of finite transformation semigroups with a strong emphasis on concrete examples and combinatorial applications. It covers the following topics on the examples of the three classical finite transformation semigroups: transformations and semigroups, ideals and Green's relations, subsemigroups, congruences, endomorphisms, nilpotent subsemigroups, presentations, actions on sets, linear representations, cross-sections and variants. The book contains many exercises and historical comments and is directed, first of all, to both graduate and postgraduate students looking for an introduction to the theory of transformation semigroups, but should also prove useful to tutors and researchers Nota de contenido: Ordinary and Partial Transformations -- The Semigroups T n, PT n, and IS n -- Generating Systems -- Ideals and Green ' s Relations -- Subgroups and Subsemigroups -- Other Relations on Semigroups -- Endomorphisms -- Nilpotent Subsemigroups -- Presentation -- Transitive Actions -- Linear Representations -- Cross-Sections -- Variants -- Order-Related Subsemigroups En línea: http://dx.doi.org/10.1007/978-1-84800-281-4 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=33977 Classical Finite Transformation Semigroups : An Introduction [documento electrónico] / Ganyushkin, Olexandr ; SpringerLink (Online service) ; Mazorchuk, Volodymyr . - London : Springer London : Imprint: Springer, 2009 . - : online resource. - (Algebra and Applications, ISSN 1572-5553; 9) .
ISBN : 978-1-84800-281-4
Idioma : Inglés (eng)
Palabras clave: Mathematics Group theory Combinatorics Theory and Generalizations Clasificación: 51 Matemáticas Resumen: The aim of this monograph is to give a self-contained introduction to the modern theory of finite transformation semigroups with a strong emphasis on concrete examples and combinatorial applications. It covers the following topics on the examples of the three classical finite transformation semigroups: transformations and semigroups, ideals and Green's relations, subsemigroups, congruences, endomorphisms, nilpotent subsemigroups, presentations, actions on sets, linear representations, cross-sections and variants. The book contains many exercises and historical comments and is directed, first of all, to both graduate and postgraduate students looking for an introduction to the theory of transformation semigroups, but should also prove useful to tutors and researchers Nota de contenido: Ordinary and Partial Transformations -- The Semigroups T n, PT n, and IS n -- Generating Systems -- Ideals and Green ' s Relations -- Subgroups and Subsemigroups -- Other Relations on Semigroups -- Endomorphisms -- Nilpotent Subsemigroups -- Presentation -- Transitive Actions -- Linear Representations -- Cross-Sections -- Variants -- Order-Related Subsemigroups En línea: http://dx.doi.org/10.1007/978-1-84800-281-4 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=33977 Ejemplares
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Título : Graded Syzygies Tipo de documento: documento electrónico Autores: Peeva, Irena ; SpringerLink (Online service) Editorial: London : Springer London Fecha de publicación: 2011 Colección: Algebra and Applications, ISSN 1572-5553 num. 14 Número de páginas: XII, 304 p Il.: online resource ISBN/ISSN/DL: 978-0-85729-177-6 Idioma : Inglés (eng) Palabras clave: Mathematics Commutative algebra rings Rings and Algebras Clasificación: 51 Matemáticas Resumen: The study of free resolutions is a core and beautiful area in Commutative Algebra. The main goal of this book is to inspire the readers and develop their intuition about syzygies and Hilbert functions. Many examples are given in order to illustrate ideas and key concepts. A valuable feature of the book is the inclusion of open problems and conjectures; these provide a glimpse of exciting, and often challenging, research directions in the field. Three types of problems are presented: Conjectures, Problems, and Open-Ended Problems. The latter do not describe specific problems but point to interesting directions for exploration. The first part of the monograph contains basic background material on graded free resolutions. Further coverage of topics includes syzygies over a polynomial ring, resolutions over quotient rings, lex ideals and Hilbert functions, compression, resolutions of monomial ideals, and syzygies of toric ideals. With a clear and self-contained exposition this text is intended for advanced graduate students and postdoctorates; it will be also of interest to senior mathematicians Nota de contenido: Graded Free Resolutions -- Hilbert Functions -- Monomial Resolutions -- Syzygies of Toric Ideals En línea: http://dx.doi.org/10.1007/978-0-85729-177-6 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=33124 Graded Syzygies [documento electrónico] / Peeva, Irena ; SpringerLink (Online service) . - London : Springer London, 2011 . - XII, 304 p : online resource. - (Algebra and Applications, ISSN 1572-5553; 14) .
ISBN : 978-0-85729-177-6
Idioma : Inglés (eng)
Palabras clave: Mathematics Commutative algebra rings Rings and Algebras Clasificación: 51 Matemáticas Resumen: The study of free resolutions is a core and beautiful area in Commutative Algebra. The main goal of this book is to inspire the readers and develop their intuition about syzygies and Hilbert functions. Many examples are given in order to illustrate ideas and key concepts. A valuable feature of the book is the inclusion of open problems and conjectures; these provide a glimpse of exciting, and often challenging, research directions in the field. Three types of problems are presented: Conjectures, Problems, and Open-Ended Problems. The latter do not describe specific problems but point to interesting directions for exploration. The first part of the monograph contains basic background material on graded free resolutions. Further coverage of topics includes syzygies over a polynomial ring, resolutions over quotient rings, lex ideals and Hilbert functions, compression, resolutions of monomial ideals, and syzygies of toric ideals. With a clear and self-contained exposition this text is intended for advanced graduate students and postdoctorates; it will be also of interest to senior mathematicians Nota de contenido: Graded Free Resolutions -- Hilbert Functions -- Monomial Resolutions -- Syzygies of Toric Ideals En línea: http://dx.doi.org/10.1007/978-0-85729-177-6 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=33124 Ejemplares
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Título : Group and Ring Theoretic Properties of Polycyclic Groups Tipo de documento: documento electrónico Autores: Wehrfritz, B.A.F ; SpringerLink (Online service) Editorial: London : Springer London Fecha de publicación: 2009 Colección: Algebra and Applications, ISSN 1572-5553 num. 10 Número de páginas: VIII, 128 p Il.: online resource ISBN/ISSN/DL: 978-1-84882-941-1 Idioma : Inglés (eng) Palabras clave: Mathematics Associative rings Rings (Algebra) Commutative algebra Group theory Theory and Generalizations Algebras Clasificación: 51 Matemáticas Resumen: Polycyclic groups are built from cyclic groups in a specific way. They arise in many contexts within group theory itself but also more generally in algebra, for example in the theory of Noetherian rings. They also touch on some aspects of topology, geometry and number theory. The first half of this book develops the standard group theoretic techniques for studying polycyclic groups and the basic properties of these groups. The second half then focuses specifically on the ring theoretic properties of polycyclic groups and their applications, often to purely group theoretic situations. The book is not intended to be encyclopedic. Instead, it is a study manual for graduate students and researchers coming into contact with polycyclic groups, where the main lines of the subject can be learned from scratch by any reader who has been exposed to some undergraduate algebra, especially groups, rings and vector spaces. Thus the book has been kept short and readable with a view that it can be read and worked through from cover to cover. At the end of each topic covered there is a description without proofs, but with full references, of further developments in the area. The book then concludes with an extensive bibliography of items relating to polycyclic groups Nota de contenido: Some Basic Group Theory -- The Basic Theory of Polycyclic Groups -- Some Ring Theory -- Soluble Linear Groups -- Further Group-Theoretic Properties of Polycyclic Groups -- Hypercentral Groups and Rings -- Groups Acting on Finitely Generated Commutative Rings -- Prime Ideals in Polycyclic Group Rings -- The Structure of Modules over Polycyclic Groups -- Semilinear and Skew Linear Groups En línea: http://dx.doi.org/10.1007/978-1-84882-941-1 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=33991 Group and Ring Theoretic Properties of Polycyclic Groups [documento electrónico] / Wehrfritz, B.A.F ; SpringerLink (Online service) . - London : Springer London, 2009 . - VIII, 128 p : online resource. - (Algebra and Applications, ISSN 1572-5553; 10) .
ISBN : 978-1-84882-941-1
Idioma : Inglés (eng)
Palabras clave: Mathematics Associative rings Rings (Algebra) Commutative algebra Group theory Theory and Generalizations Algebras Clasificación: 51 Matemáticas Resumen: Polycyclic groups are built from cyclic groups in a specific way. They arise in many contexts within group theory itself but also more generally in algebra, for example in the theory of Noetherian rings. They also touch on some aspects of topology, geometry and number theory. The first half of this book develops the standard group theoretic techniques for studying polycyclic groups and the basic properties of these groups. The second half then focuses specifically on the ring theoretic properties of polycyclic groups and their applications, often to purely group theoretic situations. The book is not intended to be encyclopedic. Instead, it is a study manual for graduate students and researchers coming into contact with polycyclic groups, where the main lines of the subject can be learned from scratch by any reader who has been exposed to some undergraduate algebra, especially groups, rings and vector spaces. Thus the book has been kept short and readable with a view that it can be read and worked through from cover to cover. At the end of each topic covered there is a description without proofs, but with full references, of further developments in the area. The book then concludes with an extensive bibliography of items relating to polycyclic groups Nota de contenido: Some Basic Group Theory -- The Basic Theory of Polycyclic Groups -- Some Ring Theory -- Soluble Linear Groups -- Further Group-Theoretic Properties of Polycyclic Groups -- Hypercentral Groups and Rings -- Groups Acting on Finitely Generated Commutative Rings -- Prime Ideals in Polycyclic Group Rings -- The Structure of Modules over Polycyclic Groups -- Semilinear and Skew Linear Groups En línea: http://dx.doi.org/10.1007/978-1-84882-941-1 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=33991 Ejemplares
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Título : Group Identities on Units and Symmetric Units of Group Rings Tipo de documento: documento electrónico Autores: Lee, Gregory T ; SpringerLink (Online service) Editorial: London : Springer London Fecha de publicación: 2010 Colección: Algebra and Applications, ISSN 1572-5553 num. 12 Número de páginas: XII, 196 p Il.: online resource ISBN/ISSN/DL: 978-1-84996-504-0 Idioma : Inglés (eng) Palabras clave: Mathematics Associative rings Rings (Algebra) Group theory and Algebras Theory Generalizations Clasificación: 51 Matemáticas Resumen: Let FG be the group ring of a group G over a field F. Write U(FG) for the group of units of FG. It is an important problem to determine the conditions under which U(FG) satisfies a group identity. In the mid 1990s, a conjecture of Hartley was verified, namely, if U(FG) satisfies a group identity, and G is torsion, then FG satisfies a polynomial identity. Necessary and sufficient conditions for U(FG) to satisfy a group identity soon followed. Since the late 1990s, many papers have been devoted to the study of the symmetric units; that is, those units u satisfying u* = u, where * is the involution on FG defined by sending each element of G to its inverse. The conditions under which these symmetric units satisfy a group identity have now been determined. This book presents these results for arbitrary group identities, as well as the conditions under which the unit group or the set of symmetric units satisfies several particular group identities of interest Nota de contenido: Group Identities on Units of Group Rings -- Group Identities on Symmetric Units -- Lie Identities on Symmetric Elements -- Nilpotence of and En línea: http://dx.doi.org/10.1007/978-1-84996-504-0 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=33656 Group Identities on Units and Symmetric Units of Group Rings [documento electrónico] / Lee, Gregory T ; SpringerLink (Online service) . - London : Springer London, 2010 . - XII, 196 p : online resource. - (Algebra and Applications, ISSN 1572-5553; 12) .
ISBN : 978-1-84996-504-0
Idioma : Inglés (eng)
Palabras clave: Mathematics Associative rings Rings (Algebra) Group theory and Algebras Theory Generalizations Clasificación: 51 Matemáticas Resumen: Let FG be the group ring of a group G over a field F. Write U(FG) for the group of units of FG. It is an important problem to determine the conditions under which U(FG) satisfies a group identity. In the mid 1990s, a conjecture of Hartley was verified, namely, if U(FG) satisfies a group identity, and G is torsion, then FG satisfies a polynomial identity. Necessary and sufficient conditions for U(FG) to satisfy a group identity soon followed. Since the late 1990s, many papers have been devoted to the study of the symmetric units; that is, those units u satisfying u* = u, where * is the involution on FG defined by sending each element of G to its inverse. The conditions under which these symmetric units satisfy a group identity have now been determined. This book presents these results for arbitrary group identities, as well as the conditions under which the unit group or the set of symmetric units satisfies several particular group identities of interest Nota de contenido: Group Identities on Units of Group Rings -- Group Identities on Symmetric Units -- Lie Identities on Symmetric Elements -- Nilpotence of and En línea: http://dx.doi.org/10.1007/978-1-84996-504-0 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=33656 Ejemplares
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Título : On Normalized Integral Table Algebras (Fusion Rings) : Generated by a Faithful Non-real Element of Degree 3 Tipo de documento: documento electrónico Autores: Zvi Arad ; SpringerLink (Online service) ; Xu Bangteng ; Chen, Guiyun ; Cohen, Effi ; Haj Ihia Hussam, Arisha ; Muzychuk, Mikhail Editorial: London : Springer London Fecha de publicación: 2011 Otro editor: Imprint: Springer Colección: Algebra and Applications, ISSN 1572-5553 num. 16 Número de páginas: X, 274 p Il.: online resource ISBN/ISSN/DL: 978-0-85729-850-8 Idioma : Inglés (eng) Palabras clave: Mathematics Algebra Commutative algebra rings Group theory Combinatorics Graph Rings and Algebras Theory Generalizations Clasificación: 51 Matemáticas Resumen: The theory of table algebras was introduced in 1991 by Z. Arad and H.Blau in order to treat, in a uniform way, products of conjugacy classes and irreducible characters of finite groups. Today, table algebra theory is a well-established branch of modern algebra with various applications, including the representation theory of finite groups, algebraic combinatorics and fusion rules algebras. This book presents the latest developments in this area. Its main goal is to give a classification of the Normalized Integral Table Algebras (Fusion Rings) generated by a faithful non-real element of degree 3. Divided into 4 parts, the first gives an outline of the classification approach, while remaining parts separately treat special cases that appear during classification. A particularly unique contribution to the field, can be found in part four, whereby a number of the algebras are linked to the polynomial irreducible representations of the group SL3(C). This book will be of interest to research mathematicians and PhD students working in table algebras, group representation theory, algebraic combinatorics and integral fusion rule algebras Nota de contenido: Introduction -- Splitting the Main Problem into Four Sub-cases -- A Proof of a Non-existence Sub-case (2) -- Preliminary Classification of Sub-case (2) -- Finishing the Proofs of the Main Results En línea: http://dx.doi.org/10.1007/978-0-85729-850-8 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=33136 On Normalized Integral Table Algebras (Fusion Rings) : Generated by a Faithful Non-real Element of Degree 3 [documento electrónico] / Zvi Arad ; SpringerLink (Online service) ; Xu Bangteng ; Chen, Guiyun ; Cohen, Effi ; Haj Ihia Hussam, Arisha ; Muzychuk, Mikhail . - London : Springer London : Imprint: Springer, 2011 . - X, 274 p : online resource. - (Algebra and Applications, ISSN 1572-5553; 16) .
ISBN : 978-0-85729-850-8
Idioma : Inglés (eng)
Palabras clave: Mathematics Algebra Commutative algebra rings Group theory Combinatorics Graph Rings and Algebras Theory Generalizations Clasificación: 51 Matemáticas Resumen: The theory of table algebras was introduced in 1991 by Z. Arad and H.Blau in order to treat, in a uniform way, products of conjugacy classes and irreducible characters of finite groups. Today, table algebra theory is a well-established branch of modern algebra with various applications, including the representation theory of finite groups, algebraic combinatorics and fusion rules algebras. This book presents the latest developments in this area. Its main goal is to give a classification of the Normalized Integral Table Algebras (Fusion Rings) generated by a faithful non-real element of degree 3. Divided into 4 parts, the first gives an outline of the classification approach, while remaining parts separately treat special cases that appear during classification. A particularly unique contribution to the field, can be found in part four, whereby a number of the algebras are linked to the polynomial irreducible representations of the group SL3(C). This book will be of interest to research mathematicians and PhD students working in table algebras, group representation theory, algebraic combinatorics and integral fusion rule algebras Nota de contenido: Introduction -- Splitting the Main Problem into Four Sub-cases -- A Proof of a Non-existence Sub-case (2) -- Preliminary Classification of Sub-case (2) -- Finishing the Proofs of the Main Results En línea: http://dx.doi.org/10.1007/978-0-85729-850-8 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=33136 Ejemplares
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