McKenzie, Ralph N.; McNulty, George F.; Taylor, Walter F. 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]. Cited in 2 ReviewsCited in 5 Documents 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 Keywords:congruences; lattices; direct join decomposition; modular lattices of finite height; clones; subdirect representations; monadic algebras; projective geometries; congruence lattices; commutator; unique factorization of algebras; finite algebras; indecomposable algebras; refinement property Citations:Zbl 0611.08001 PDFBibTeX XMLCite \textit{R. N. McKenzie} et al., Algebras, lattices, varieties. Volume I. With an additional bibliography. Reprint of the 1987 original published by Wadsworth \& Brooks/Cole Advanced Books \& Software. Providence, RI: AMS Chelsea Publishing (2018; Zbl 1392.08001) Full Text: DOI