Advances in the Theory of Varieties of Semigroups

Edmond W. H. Lee (Autor)

Buch | Softcover

XV, 287 Seiten

2023 | 1st ed. 2023
Springer International Publishing (Verlag)
978-3-031-16496-5 (ISBN)

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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.

lt;b>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 mainly interested in the theory of varieties of semigroups-a topic that belongs to the intersection of universal algebra and semigroup theory-and is most 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.

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.

"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)

“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)

Erscheinungsdatum	11.04.2023
Reihe/Serie	Frontiers in Mathematics
Zusatzinfo	XV, 287 p. 16 illus.
Verlagsort	Cham
Sprache	englisch
Maße	168 x 240 mm
Gewicht	511 g
Themenwelt	Mathematik / Informatik ► Mathematik ► Algebra
Schlagworte	Aperiodic monoids • Aperiodic Rees-Suschkewitsch varieties • Classical semigroups • Cross variety • Finite based involution semigroups • Finite identity basis • Hereditarily finitely based • Involution semigroup • Irredundant identity basis • Lattice of varieties • Lattice varieties semigroups • Limit variety • Monoid • Monoids • Pollak Volkov semigroups • Rees quotients free monoids • Rees-Suschkewitsch variety • Rees–Suschkewitsch variety • Semigroup • semigroups • Semigroup varieties • Semigroup variety • Semigroup vs monoids • universal algebra
ISBN-10	3-031-16496-2 / 3031164962
ISBN-13	978-3-031-16496-5 / 9783031164965
Zustand	Neuware