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Algebras, lattices, varieties. Volume I. With an additional bibliography. Reprint of the 1987 original published by Wadsworth & Brooks/Cole Advanced Books & Software. (English) Zbl 1392.08001

Providence, RI: AMS Chelsea Publishing (ISBN 978-1-4704-4295-8/hbk; 978-1-4704-4719-9/ebook). xii, 367 p. (2018).
Publisher’s 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.
See the review of the 1987 original in [Zbl 0611.08001].

MSC:

08-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to general algebraic systems
06-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to ordered structures
08A30 Subalgebras, congruence relations
08B10 Congruence modularity, congruence distributivity
06C05 Modular lattices, Desarguesian lattices
06B05 Structure theory of lattices
06C20 Complemented modular lattices, continuous geometries
08Axx Algebraic structures
08Bxx Varieties

Citations:

Zbl 0611.08001
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