SelectedWorks - Edmond W. H. Lee

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Selected Works of Edmond W. H. Lee

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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.

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About Edmond W. H. Lee

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.

Advances in the Theory of Varieties of Semigroups (Edmond W. H. Lee) Mathematics Faculty Books and Book Chapters (2023)

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 ...

Single-Authored Articles (43)

Embedding Finite Involution Semigroups in Matrices with Transposition (Edmond W. H. Lee) Discrete Applied Mathematics (2023)

The present article establishes two contrasting results: a finite involution semigroup is embeddable in some semigroup of complex matrices with conjugate transposition if and only if it is an inverse semigroup, while every finite involution ...

A Minimal Pseudo-complex Monoid (Edmond W. H. Lee) Archiv der Mathematik (2023)

A monoid is pseudo-complex if the semigroup variety it generates has uncountably many subvarieties, while the monoid variety it generates has only finitely many subvarieties. The smallest pseudo-complex monoid currently known is of order seven. ...

Intervals of varieties of involution semigroups with contrasting reduct intervals (Edmond W. H. Lee) Bollettino dell'Unione Matematica Italiana (2022)

It is known that the lattice structure of an interval of varieties of involution semigroups can be very different from that of its reduct interval of varieties of semigroups, but it is uncertain how wide ...

Join irreducible 2-testable semigroups (Edmond W. H. Lee) Discussiones Mathematicae - General Algebra and Applications (2021)

A nontrivial pseudovariety is join irreducible if whenever it is contained in the complete join of some collection of pseudovarieties, then it is contained in one of the pseudovarieties. A finite semigroup is join irreducible ...

Non-Specht variety generated by an involution semigroup of order five (Edmond W. H. Lee) Transactions of the Moscow Mathematical Society (2020)

The non-orthodox 0-simple semigroup A2 of order five admits a unary operation under which it is an involution semigroup. It is known that A2 generates a Specht variety of semigroups. In contrast, it is shown ...

Varieties of Involution Monoids with Extreme Properties (Edmond W. H. Lee) The Quarterly Journal of Mathematics (2019)

A variety that contains continuum many subvarieties is said to be huge. A sufficient condition is established under which an involution monoid generates a variety that is huge by virtue of its lattice of subvarieties ...

Non-finitely based finite involution semigroups with finitely based semigroup reducts (Edmond W. H. Lee) Korean Journal of Mathematics (2019)

Recently, an infinite class of finitely based finite involution semigroups with non-finitely based semigroup reducts have been found. In contrast, only one example of the opposite type---non-finitely based finite involution semigroups with finitely based semigroup ...

Locally Finite Monoids in Finitely Based Varieties (Edmond W. H. Lee) Logic Journal of the IGPL (2019)

It is shown that given any finite system of monoid identities, it is decidable if the class of locally finite monoids that satisfy the system is a variety. This answers an open problem of Mark ...

Variety Membership Problem for Two Classes of Non-Finitely Based Semigroups (Edmond W. H. Lee) Wuhan University Journal of Natural Sciences (2018)

The variety membership problem for two classes of non-finitely based semigroups is considered. It is shown that a finite semigroup S belongs to the variety generated by one of these non-finitely based semigroups if and ...

A Sufficient Condition for the Absence of Irredundant Bases (Edmond W. H. Lee) Houston Journal of Mathematics (2018)

A basis of identities for an algebra is irredundant if each of its proper subsets fails to be a basis. A sufficient condition is established under which a non-finitely based finite algebra of finite type ...

Varieties generated by unstable involution semigroups with continuum many subvarieties (Edmond W. H. Lee) Comptes Rendus Mathematique (2018)

Over the years, several finite semigroups have been found to generate varieties with continuum many subvarieties. However, finite involution semigroups that generate varieties with continuum many subvarieties seem much rarer; in fact, only one example—an ...

On a Class of Completely Join Prime J-Trivial Semigroups with Unique Involution (Edmond W. H. Lee) Algebra Universalis (2017)

A finite algebra is completely join prime if whenever it belongs to the complete join of some collection of pseudovarieties, then it belongs to one of the pseudovarieties. An infinite class of completely join prime ...

Equational Theories of Unstable Involution Semigroups (Edmond W. H. Lee) Electronic Research Announcements in Mathematical Sciences (2017)

It is long known that with respect to the property of having a finitely axiomatizable equational theory, there is no relationship between a general involution semigroup and its semigroup reduct. The present article establishes such ...

Finite Involution Semigroups with Infinite Irredundant Bases of Identities (Edmond W. H. Lee) Forum Mathematicum (2016)

A basis of identities for an algebra is irredundant if each of its proper subsets fails to be a basis for the algebra. The first known examples of finite involution semigroups with infinite irredundant bases ...

Finitely Based Finite Involution Semigroups with Non-finitely Based Reducts (Edmond W. H. Lee) Quaestiones Mathematicae (2016)

Since the study of the finite basis problem for finite semigroups began in the 1960s, it has been unknown if there exists any finite involution semigroup that is finitely based but the reduct of which ...

A Class of Finite Semigroups Without Irredundant Bases of Identities (Edmond W. H. Lee) Yokohama Mathematical Journal (2015)

A basis of identities for an algebra is irredundant if each of its proper subsets fails to be a basis for the algebra. A new infinite class of finite semigroups without irredundant bases is exhibited. ...

Inherently Non-Finitely Generated Varieties of Aperiodic Monoids with Central Idempotents (Edmond W. H. Lee) Journal of Mathematical Sciences (2015)

Let A denote the class of aperiodic monoids with central idempotents. A subvariety of A that is not contained in any finitely generated subvariety of A is said to be inherently non-finitely generated. A characterization ...

On Certain Cross Varieties of Aperiodic Monoids with Commuting Idempotents (Edmond W. H. Lee) Results in Mathematics (2014)

Let Acom denote the class of aperiodic monoids with commuting idempotents. It is shown that any subvariety of Acom that satisfies the identity x2yx ≈ xyx2 is Cross if and only if it excludes the ...

On a Question of Pollák and Volkov Regarding Hereditarily Finitely Based Identities (Edmond W. H. Lee) Periodica Mathematica Hungarica (2014)

A semigroup identity is alternating if it is formed by a simple word and an almost simple word. A complete description of all hereditarily finitely based, alternating identities is presented. This answers a question of ...

Finite Basis Problem for the Direct Product of Some J-Trivial Monoid with Groups of Finite Exponent (Edmond W. H. Lee) Vestnik Sankt-Peterburgskogo Universiteta. Seriya 1. Matematika, Mekhanika, Astronomiya (2013)

It is proved that the direct product of the J-trivial monoid S(xyx) with any noncommutative group of finite exponent is non-finitely based. This result provides new, simpler examples of two finitely based finite monoids for ...

Finitely Based Monoids Obtained From Non-Finitely Based Semigroups (Edmond W. H. Lee) Universitatis Iagellonicae Acta Mathematica (2013)

Presently, no example of non-finitely based finite semigroup S is known for which the monoid S1 is finitely based. Based on a general result of M. V. Volkov, two methods are established from which examples ...

Almost Cross Varieties of Aperiodic Monoids with Central Idempotents (Edmond W. H. Lee) Beiträge zur Algebra und Geometrie (2013)

It is known that the class A of aperiodic monoids with central idempotents contains precisely two finitely generated, almost Cross subvarieties. The present article exhibits the first example of a non-finitely generated, almost Cross subvariety ...

Finite Basis Problem for Semigroups of Order Five or Less: Generalization and Revisitation (Edmond W. H. Lee) Studia Logica (2013)

A system of semigroup identities is hereditarily finitely based if it defines a variety all semigroups of which are finitely based. Two new types of hereditarily finitely based identity systems are presented. Two of these ...

A Sufficient Condition for the Non-Finite Basis Property of Semigroups (Edmond W. H. Lee) Monatshefte für Mathematik (2012)

Recently, Zhang and Luo proved that a certain semigroup L of order six is non-finitely based. The main aim of the present article is to generalize this result to a sufficient condition for the non-finite ...