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Título : Dualisability : Unary Algebras and Beyond Tipo de documento: documento electrónico Autores: Pitkethly, Jane ; SpringerLink (Online service) ; Davey, Brian Editorial: Boston, MA : Springer US Fecha de publicación: 2005 Colección: Advances in Mathematics num. 9 Número de páginas: XII, 264 p. 38 illus Il.: online resource ISBN/ISSN/DL: 978-0-387-27570-3 Idioma : Inglés (eng) Palabras clave: Mathematics Science Algebra Ordered algebraic structures Combinatorics General Algebraic Systems Order, Lattices, Structures Science, general Clasificación: 51 Matemáticas Resumen: Natural duality theory is one of the major growth areas within general algebra. This text provides a short path to the forefront of research in duality theory. It presents a coherent approach to new results in the area, as well as exposing open problems. Unary algebras play a special role throughout the text. Individual unary algebras are relatively simple and easy to work with. But as a class they have a rich and complex entanglement with dualisability. This combination of local simplicity and global complexity ensures that, for the study of natural duality theory, unary algebras are an excellent source of examples and counterexamples. A number of results appear here for the first time. In particular, the text ends with an appendix that provides a new and definitive approach to the concept of the rank of a finite algebra and its relationship with strong dualisability. Audience This book is intended for established researchers in natural duality theory, general algebraists wishing to commence research in duality theory, and graduate students in algebra Nota de contenido: Unary algebras and dualisability -- Binary homomorphisms and natural dualities -- The complexity of dualisability: three-element unary algebras -- Full and strong dualisability: three-element unary algebras -- Dualisability and algebraic constructions -- Dualisability and clones -- Inherent dualisability En línea: http://dx.doi.org/10.1007/0-387-27570-3 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=35124 Dualisability : Unary Algebras and Beyond [documento electrónico] / Pitkethly, Jane ; SpringerLink (Online service) ; Davey, Brian . - Boston, MA : Springer US, 2005 . - XII, 264 p. 38 illus : online resource. - (Advances in Mathematics; 9) .
ISBN : 978-0-387-27570-3
Idioma : Inglés (eng)
Palabras clave: Mathematics Science Algebra Ordered algebraic structures Combinatorics General Algebraic Systems Order, Lattices, Structures Science, general Clasificación: 51 Matemáticas Resumen: Natural duality theory is one of the major growth areas within general algebra. This text provides a short path to the forefront of research in duality theory. It presents a coherent approach to new results in the area, as well as exposing open problems. Unary algebras play a special role throughout the text. Individual unary algebras are relatively simple and easy to work with. But as a class they have a rich and complex entanglement with dualisability. This combination of local simplicity and global complexity ensures that, for the study of natural duality theory, unary algebras are an excellent source of examples and counterexamples. A number of results appear here for the first time. In particular, the text ends with an appendix that provides a new and definitive approach to the concept of the rank of a finite algebra and its relationship with strong dualisability. Audience This book is intended for established researchers in natural duality theory, general algebraists wishing to commence research in duality theory, and graduate students in algebra Nota de contenido: Unary algebras and dualisability -- Binary homomorphisms and natural dualities -- The complexity of dualisability: three-element unary algebras -- Full and strong dualisability: three-element unary algebras -- Dualisability and algebraic constructions -- Dualisability and clones -- Inherent dualisability En línea: http://dx.doi.org/10.1007/0-387-27570-3 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=35124 Ejemplares
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Título : M-Solid Varieties of Algebras Tipo de documento: documento electrónico Autores: Koppitz, J ; SpringerLink (Online service) ; Denecke, K Editorial: Boston, MA : Springer US Fecha de publicación: 2006 Colección: Advances in Mathematics num. 10 Número de páginas: XIV, 342 p Il.: online resource ISBN/ISSN/DL: 978-0-387-30806-7 Idioma : Inglés (eng) Palabras clave: Mathematics Programming languages (Electronic computers) Mathematical logic Algebra Group theory Ordered algebraic structures General Algebraic Systems Theory and Generalizations Order, Lattices, Structures Languages, Compilers, Interpreters Logic Formal Languages Clasificación: 51 Matemáticas Resumen: M-Solid Varieties of Algebras provides a complete and systematic introduction to the fundamentals of the hyperequational theory of universal algebra, offering the newest results on M-solid varieties of semirings and semigroups. The book aims to develop the theory of M-solid varieties as a system of mathematical discourse that is applicable in several concrete situations. It applies the general theory to two classes of algebraic structures, semigroups and semirings. Both these varieties and their subvarieties play an important role in computer science. A unique feature of this book is the use of Galois connections to integrate different topics. Galois connections form the abstract framework not only for classical and modern Galois theory, involving groups, fields and rings, but also for many other algebraic, topological, ordertheoretical, categorical and logical theories. This concept is used throughout the whole book, along with the related topics of closure operators, complete lattices, Galois closed subrelations and conjugate pairs of completely additive closure operators. Audience This book is intended for researchers in the fields of universal algebra, semigroups, and semirings; researchers in theoretical computer science; and students and lecturers in these fields Nota de contenido: Basic Concepts -- Closure Operators and Lattices -- M-Hyperidentities and M-solid Varieties -- Hyperidentities and Clone Identities -- Solid Varieties of Arbitrary Type -- Monoids of Hypersubstitutions -- M-Solid Varieties of Semigroups -- M-solid Varieties of Semirings En línea: http://dx.doi.org/10.1007/0-387-30806-7 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=34774 M-Solid Varieties of Algebras [documento electrónico] / Koppitz, J ; SpringerLink (Online service) ; Denecke, K . - Boston, MA : Springer US, 2006 . - XIV, 342 p : online resource. - (Advances in Mathematics; 10) .
ISBN : 978-0-387-30806-7
Idioma : Inglés (eng)
Palabras clave: Mathematics Programming languages (Electronic computers) Mathematical logic Algebra Group theory Ordered algebraic structures General Algebraic Systems Theory and Generalizations Order, Lattices, Structures Languages, Compilers, Interpreters Logic Formal Languages Clasificación: 51 Matemáticas Resumen: M-Solid Varieties of Algebras provides a complete and systematic introduction to the fundamentals of the hyperequational theory of universal algebra, offering the newest results on M-solid varieties of semirings and semigroups. The book aims to develop the theory of M-solid varieties as a system of mathematical discourse that is applicable in several concrete situations. It applies the general theory to two classes of algebraic structures, semigroups and semirings. Both these varieties and their subvarieties play an important role in computer science. A unique feature of this book is the use of Galois connections to integrate different topics. Galois connections form the abstract framework not only for classical and modern Galois theory, involving groups, fields and rings, but also for many other algebraic, topological, ordertheoretical, categorical and logical theories. This concept is used throughout the whole book, along with the related topics of closure operators, complete lattices, Galois closed subrelations and conjugate pairs of completely additive closure operators. Audience This book is intended for researchers in the fields of universal algebra, semigroups, and semirings; researchers in theoretical computer science; and students and lecturers in these fields Nota de contenido: Basic Concepts -- Closure Operators and Lattices -- M-Hyperidentities and M-solid Varieties -- Hyperidentities and Clone Identities -- Solid Varieties of Arbitrary Type -- Monoids of Hypersubstitutions -- M-Solid Varieties of Semigroups -- M-solid Varieties of Semirings En línea: http://dx.doi.org/10.1007/0-387-30806-7 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=34774 Ejemplares
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Título : Ordered Sets Tipo de documento: documento electrónico Autores: Harzheim, Egbert ; SpringerLink (Online service) Editorial: Boston, MA : Springer US Fecha de publicación: 2005 Colección: Advances in Mathematics num. 7 Número de páginas: XII, 386 p Il.: online resource ISBN/ISSN/DL: 978-0-387-24222-4 Idioma : Inglés (eng) Palabras clave: Mathematics Algebra Ordered algebraic structures Order, Lattices, Algebraic Structures Clasificación: 51 Matemáticas Resumen: The textbook literature on ordered sets is still rather limited. A lot of material is presented in this book that appears now for the first time in a textbook. Order theory works with combinatorial and set-theoretical methods, depending on whether the sets under consideration are finite or infinite. In this book the set-theoretical parts prevail. The book treats in detail lexicographic products and their connections with universally ordered sets, and further it gives thorough investigations on the structure of power sets. Other topics dealt with include dimension theory of ordered sets, well-quasi-ordered sets, trees, combinatorial set theory for ordered sets, comparison of order types, and comparibility graphs. Audience This book is intended for mathematics students and for mathemeticians who are interested in set theory. Only some fundamental parts of naïve set theory are presupposed. Since all proofs are worked out in great detail, the book should be suitable as a text for a course on order theory Nota de contenido: Fundamental notions of set theory -- Fundamental notions -- General relations between posets and their chains and antichains -- Linearly ordered sets -- Products of orders -- Universally ordered sets -- Applications of the splitting method -- The dimension of posets -- Well-founded posets, pwo-sets and trees -- On the order structure of power sets -- Comparison of order types -- Comparability graphs En línea: http://dx.doi.org/10.1007/b104891 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=35079 Ordered Sets [documento electrónico] / Harzheim, Egbert ; SpringerLink (Online service) . - Boston, MA : Springer US, 2005 . - XII, 386 p : online resource. - (Advances in Mathematics; 7) .
ISBN : 978-0-387-24222-4
Idioma : Inglés (eng)
Palabras clave: Mathematics Algebra Ordered algebraic structures Order, Lattices, Algebraic Structures Clasificación: 51 Matemáticas Resumen: The textbook literature on ordered sets is still rather limited. A lot of material is presented in this book that appears now for the first time in a textbook. Order theory works with combinatorial and set-theoretical methods, depending on whether the sets under consideration are finite or infinite. In this book the set-theoretical parts prevail. The book treats in detail lexicographic products and their connections with universally ordered sets, and further it gives thorough investigations on the structure of power sets. Other topics dealt with include dimension theory of ordered sets, well-quasi-ordered sets, trees, combinatorial set theory for ordered sets, comparison of order types, and comparibility graphs. Audience This book is intended for mathematics students and for mathemeticians who are interested in set theory. Only some fundamental parts of naïve set theory are presupposed. Since all proofs are worked out in great detail, the book should be suitable as a text for a course on order theory Nota de contenido: Fundamental notions of set theory -- Fundamental notions -- General relations between posets and their chains and antichains -- Linearly ordered sets -- Products of orders -- Universally ordered sets -- Applications of the splitting method -- The dimension of posets -- Well-founded posets, pwo-sets and trees -- On the order structure of power sets -- Comparison of order types -- Comparability graphs En línea: http://dx.doi.org/10.1007/b104891 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=35079 Ejemplares
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Título : Regularity Properties of Functional Equations in Several Variables Tipo de documento: documento electrónico Autores: Járai, Antal ; SpringerLink (Online service) Editorial: Boston, MA : Springer US Fecha de publicación: 2005 Colección: Advances in Mathematics num. 8 Número de páginas: IX, 363 p Il.: online resource ISBN/ISSN/DL: 978-0-387-24414-3 Idioma : Inglés (eng) Palabras clave: Mathematics Difference equations Functional and Equations Clasificación: 51 Matemáticas Resumen: This book is about regularity properties of functional equations. In the second part of his fifth problem, Hilbert asked, concerning functional equations, "In how far are the assertions which we can make in the case of differentiable functions true under proper modifications without this assumption?” This book contains, in a unified fashion, most of the modern results about regularity of non-composite functional equations with several variables. These results show that "weak” regularity properties, say measurability or continuity, of solutions imply that they are in C[infinity], and hence the equation can be reduced to a differential equation. A long introduction highlights the basic ideas for beginners. Several applications are also included. Audience This book is intended for researchers in the fields of mathematical analysis, applied mathematics, theoretical economics, and statistics Nota de contenido: Preliminaries -- Steinhaus Type Theorems -- Boundedness and Continuity of Solutions -- Differentiability and Analyticity -- Regularity Theorems on Manifolds -- Regularity Results with Fewer Variables -- Applications En línea: http://dx.doi.org/10.1007/b105379 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=35087 Regularity Properties of Functional Equations in Several Variables [documento electrónico] / Járai, Antal ; SpringerLink (Online service) . - Boston, MA : Springer US, 2005 . - IX, 363 p : online resource. - (Advances in Mathematics; 8) .
ISBN : 978-0-387-24414-3
Idioma : Inglés (eng)
Palabras clave: Mathematics Difference equations Functional and Equations Clasificación: 51 Matemáticas Resumen: This book is about regularity properties of functional equations. In the second part of his fifth problem, Hilbert asked, concerning functional equations, "In how far are the assertions which we can make in the case of differentiable functions true under proper modifications without this assumption?” This book contains, in a unified fashion, most of the modern results about regularity of non-composite functional equations with several variables. These results show that "weak” regularity properties, say measurability or continuity, of solutions imply that they are in C[infinity], and hence the equation can be reduced to a differential equation. A long introduction highlights the basic ideas for beginners. Several applications are also included. Audience This book is intended for researchers in the fields of mathematical analysis, applied mathematics, theoretical economics, and statistics Nota de contenido: Preliminaries -- Steinhaus Type Theorems -- Boundedness and Continuity of Solutions -- Differentiability and Analyticity -- Regularity Theorems on Manifolds -- Regularity Results with Fewer Variables -- Applications En línea: http://dx.doi.org/10.1007/b105379 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=35087 Ejemplares
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