Algebras, Lattices, Varieties, Volume I

Ralph N. McKenzie, George F. McNulty, Walter F. Taylor

ISBN 10: 1470442957 / ISBN 13: 9781470442958

Editore: American Mathematical Society, US, 2018

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. Codice articolo LU-9781470442958

Riassunto:

McKenzie, McNulty, and Taylor begin a four-volume textbook devoted to the general theory of algebras and the closely related subject of lattice theory. Reprinted from the 1987 edition, they say, this and the second volume would provide a foundation for anyone beginning research into the general theory of algebraic systems. This first volume covers basic concepts, lattices, unary and binary operations, fundamental algebraic results, and unique factorization. They include chapter-end exercises and an additional biography with recent references. Annotation ©2018 Ringgold, Inc., Portland, OR (protoview.com)

Dati bibliografici

Titolo: Algebras, Lattices, Varieties, Volume I
Casa editrice: American Mathematical Society, US
Data di pubblicazione: 2018
Legatura: Hardback
Condizione: New