Edmond W. H. Lee

Advances in the Theory of Varieties of Semigroups (eBook, PDF)

• Format: PDF

Produktbeschreibung

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.

Produktdetails

• Verlag: Springer International Publishing
• Erscheinungstermin: 8. April 2023
• Englisch
• ISBN-13: 9783031164972
• Artikelnr.: 67755064

Autorenporträt

Edmond W. H. Lee is a professor of mathematics at Nova Southeastern University, USA. He holds a Ph.D. from Simon Fraser University, Canada, and a D.Sc. from National Research University Higher School of Economics, Russia. As a mathematician, Lee is primarily interested in the theory of varieties of semigroups—a topic that lies in the intersection of universal algebra and semigroup theory—and is best known for his work on equational theories of small semigroups. Lee is currently an active member of the editorial boards of Algebra Universalis and Semigroup Forum.

Inhaltsangabe

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.

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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.

Rezensionen

"The monograph by Edmond W. H. Lee is a significant contribution to the research of semigroup varieties and varieties of semigroups equipped with additional unary or 0-ary operations. It will undoubtedly be interesting and useful to all researchers involved in the theory of varieties of semigroups, the theory of semigroups as a whole and related branches of general algebra." (Boris M. Vernikov, Semigroup Forum, Vol. 107 (2), 2023)