Advances in the Theory of Varieties of Sem...

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Sprache: Englisch

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Beschreibung

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.

Über den Autor

¿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 [...]. 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.

Zusammenfassung

Explores varieties of semigroups, varieties of involution semigroups, and varieties of monoids

Solves previously open problems with detailed proofs while highlighting questions that remain unanswered

Presents a comprehensive overview of the subfield, featuring the major results and their full context

Inhaltsverzeichnis

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.

Details

Erscheinungsjahr:	2023
Fachbereich:	Arithmetik & Algebra
Genre:	Mathematik , Medizin , Naturwissenschaften , Technik
Rubrik:	Naturwissenschaften & Technik
Medium:	Taschenbuch
Inhalt:	xv 287 S. 16 s/w Illustr. 287 p. 16 illus.
ISBN-13:	9783031164965
ISBN-10:	3031164962
Sprache:	Englisch
Einband:	Kartoniert / Broschiert
Autor:	Lee, Edmond W. H.
Auflage:	1st edition 2023
Hersteller:	Springer Nature Switzerland Springer International Publishing
Verantwortliche Person für die EU:	Springer Basel AG in Springer Science + Business Media, Heidelberger Platz 3, D-14197 Berlin, juergen.hartmann@springer.com
Maße:	240 x 168 x 17 mm
Von/Mit:	Edmond W. H. Lee
Erscheinungsdatum:	09.04.2023
Gewicht:	0,514 kg