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Author: Ivo G. Rosenberg Publisher: Springer Science & Business Media ISBN: 9401706972 Category : Mathematics Languages : en Pages : 565
Book Description
In the summer of 1991 the Department of Mathematics and Statistics of the Universite de Montreal was fortunate to host the NATO Advanced Study Institute "Algebras and Orders" as its 30th Seminaire de mathematiques superieures (SMS), a summer school with a long tradition and well-established reputation. This book contains the contributions of the invited speakers. Universal algebra- which established itself only in the 1930's- grew from traditional algebra (e.g., groups, modules, rings and lattices) and logic (e.g., propositional calculus, model theory and the theory of relations). It started by extending results from these fields but by now it is a well-established and dynamic discipline in its own right. One of the objectives of the ASI was to cover a broad spectrum of topics in this field, and to put in evidence the natural links to, and interactions with, boolean algebra, lattice theory, topology, graphs, relations, automata, theoretical computer science and (partial) orders. The theory of orders is a relatively young and vigorous discipline sharing certain topics as well as many researchers and meetings with universal algebra and lattice theory. W. Taylor surveyed the abstract clone theory which formalizes the process of compos ing operations (i.e., the formation of term operations) of an algebra as a special category with countably many objects, and leading naturally to the interpretation and equivalence of varieties.
Author: Ivo G. Rosenberg Publisher: Springer Science & Business Media ISBN: 9401706972 Category : Mathematics Languages : en Pages : 565
Book Description
In the summer of 1991 the Department of Mathematics and Statistics of the Universite de Montreal was fortunate to host the NATO Advanced Study Institute "Algebras and Orders" as its 30th Seminaire de mathematiques superieures (SMS), a summer school with a long tradition and well-established reputation. This book contains the contributions of the invited speakers. Universal algebra- which established itself only in the 1930's- grew from traditional algebra (e.g., groups, modules, rings and lattices) and logic (e.g., propositional calculus, model theory and the theory of relations). It started by extending results from these fields but by now it is a well-established and dynamic discipline in its own right. One of the objectives of the ASI was to cover a broad spectrum of topics in this field, and to put in evidence the natural links to, and interactions with, boolean algebra, lattice theory, topology, graphs, relations, automata, theoretical computer science and (partial) orders. The theory of orders is a relatively young and vigorous discipline sharing certain topics as well as many researchers and meetings with universal algebra and lattice theory. W. Taylor surveyed the abstract clone theory which formalizes the process of compos ing operations (i.e., the formation of term operations) of an algebra as a special category with countably many objects, and leading naturally to the interpretation and equivalence of varieties.
Author: Richard D. Schafer Publisher: Courier Dover Publications ISBN: 0486164179 Category : Mathematics Languages : en Pages : 177
Book Description
Concise graduate-level introductory study presents some of the important ideas and results in the theory of nonassociative algebras. Places particular emphasis on alternative and (commutative) Jordan algebras. 1966 edition.
Author: Jorge Martínez Publisher: Springer Science & Business Media ISBN: 9781402007521 Category : Mathematics Languages : en Pages : 340
Book Description
This publication surveys some of the disciplines within ordered algebraic structures and also contains chapters highlighting a broad spectrum of research interests. In all, this book represents a reasonably accurate cross-section of the state of the art in ordered algebraic structures.
Author: Lindsay Childs Publisher: American Mathematical Soc. ISBN: 0821810774 Category : Mathematics Languages : en Pages : 133
Book Description
This volume gives two new methods for constructing $p$-elementary Hopf algebra orders over the valuation ring $R$ of a local field $K$ containing the $p$-adic rational numbers. One method constructs Hopf orders using isogenies of commutative degree 2 polynomial formal groups of dimension $n$, and is built on a systematic study of such formal group laws. The other method uses an exponential generalization of a 1992 construction of Greither. Both constructions yield Raynaud orders as iterated extensions of rank $p$ Hopf algebras; the exponential method obtains all Raynaud orders whose invariants satisfy a certain $p$-adic condition.
Author: David J. Winter Publisher: Courier Corporation ISBN: 048646282X Category : Mathematics Languages : uk Pages : 162
Book Description
Solid but concise, this account emphasizes Lie algebra's simplicity of theory, offering new approaches to major theorems and extensive treatment of Cartan and related Lie subalgebras over arbitrary fields. 1972 edition.
Author: John Voight Publisher: Springer Nature ISBN: 3030566943 Category : Mathematics Languages : en Pages : 877
Book Description
This open access textbook presents a comprehensive treatment of the arithmetic theory of quaternion algebras and orders, a subject with applications in diverse areas of mathematics. Written to be accessible and approachable to the graduate student reader, this text collects and synthesizes results from across the literature. Numerous pathways offer explorations in many different directions, while the unified treatment makes this book an essential reference for students and researchers alike. Divided into five parts, the book begins with a basic introduction to the noncommutative algebra underlying the theory of quaternion algebras over fields, including the relationship to quadratic forms. An in-depth exploration of the arithmetic of quaternion algebras and orders follows. The third part considers analytic aspects, starting with zeta functions and then passing to an idelic approach, offering a pathway from local to global that includes strong approximation. Applications of unit groups of quaternion orders to hyperbolic geometry and low-dimensional topology follow, relating geometric and topological properties to arithmetic invariants. Arithmetic geometry completes the volume, including quaternionic aspects of modular forms, supersingular elliptic curves, and the moduli of QM abelian surfaces. Quaternion Algebras encompasses a vast wealth of knowledge at the intersection of many fields. Graduate students interested in algebra, geometry, and number theory will appreciate the many avenues and connections to be explored. Instructors will find numerous options for constructing introductory and advanced courses, while researchers will value the all-embracing treatment. Readers are assumed to have some familiarity with algebraic number theory and commutative algebra, as well as the fundamentals of linear algebra, topology, and complex analysis. More advanced topics call upon additional background, as noted, though essential concepts and motivation are recapped throughout.
Author: Ralph N. McKenzie Publisher: American Mathematical Society ISBN: 1470442957 Category : Mathematics Languages : en Pages : 386
Book Description
This book presents the foundations of a general theory of algebras. Often called “universal algebra”, this theory provides a common framework for all algebraic systems, including groups, rings, modules, fields, and lattices. Each chapter is replete with useful illustrations and exercises that solidify the reader's understanding. The book begins by developing the main concepts and working tools of algebras and lattices, and continues with examples of classical algebraic systems like groups, semigroups, monoids, and categories. The essence of the book lies in Chapter 4, which provides not only basic concepts and results of general algebra, but also the perspectives and intuitions shared by practitioners of the field. The book finishes with a study of possible uniqueness of factorizations of an algebra into a direct product of directly indecomposable algebras. There is enough material in this text for a two semester course sequence, but a one semester course could also focus primarily on Chapter 4, with additional topics selected from throughout the text.
Author: Ivo G. Rosenberg
Author: Ivo G. Rosenberg
Author: Richard D. Schafer
Author: Jorge Martínez
Author: Lindsay Childs
Author: David J. Winter
Author: John Voight
Author: Ralph Douglas Doner
Author: Michiel Hazewinkel
Author: M. Pouzet
Author: Ralph N. McKenzie