Full Description
This monograph thoroughly explores the development of the theory of varieties of semigroups and of two related algebras: involution semigroups and monoids. Through this in-depth analysis, readers will attain a deeper understanding of the differences between these three types of varieties, which may otherwise seem counterintuitive. New results with detailed proofs are also presented that answer previously unsolved fundamental problems. Featuring both a comprehensive overview as well as highlighting the author's own significant contributions to the area, this book will help establish this subfield as a matter of timely interest. Advances in the Theory of Varieties of Semigroups will appeal to researchers in universal algebra and will be particularly valuable for specialists in semigroups.
Contents
Historical overview and main results.- Preliminaries. Part I - Semigroups.- Aperiodic Rees-Suschkewitsch varieties.- A problem of Pollak and Volkov on hereditarily finitely based identities.- Sufficient conditions for the non-finite basis property.- Semigroups without irredundant identity bases.- Part II - Involution Semigroups.- Involution semigroups with infinite irredundant identity bases.- Finitely based involution semigroups with non-finitely based reducts.- Counterintuitive examples of involution semigroups.- Equational theories of twisted involution semigroups.- Part III - Monoids.- Hereditarily finitely based varieties of monoids.- Varieties of aperiodic monoids with central idempotents.- Certain Cross varieties of aperiodic monoids with commuting idempotents.- Counterintuitive examples of monoids.
