SelectedWorks - Edmond W. H. Lee

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Selected Works of Edmond W. H. Lee

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Associate Professor, Department of Mathematics

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About Edmond W. H. Lee

Positions

July 2015 - Present	Associate Professor, Nova Southeastern University ‐ Department of Mathematics
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August 2011 - June 2015	Assistant Professor, Nova Southeastern University ‐ Department of Mathematics
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Disciplines

Research Interests

varieties of semigroups, lattices of varieties, and finite basis problem

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2002	Ph.D., Simon Fraser University ‐ Department of Mathematics
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1997	M.Sc., Simon Fraser University ‐ Department of Mathematics
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1994	B.Sc., University of Toronto ‐ Department of Mathematics
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Contact Information

(954) 262-8320

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ORCID

http://orcid.org/0000-0002-1662-3734

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Single-Authored Articles
Co-Authored Articles

Single-Authored Articles (35)

Peer-reviewed articles authored by Edmond W. H. Lee

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 ...

Maximal Specht Varieties of Monoids (Edmond W. H. Lee) Moscow Mathematical Journal (2012)

A variety of algebras is a Specht variety if all its subvarieties are finitely based. This article presents the first example of a maximal Specht variety of monoids. The existence of such an example is ...

Varieties Generated by 2-testable Monoids (Edmond W. H. Lee) Studia Scientiarum Mathematicarum Hungarica (2012)

The smallest monoid containing a 2-testable semigroup is defined to be a 2-testable monoid. The well-known Brandt monoid B21 of order six is an example of a 2-testable monoid. The finite basis problem for 2-testable ...

Cross Varieties of Aperiodic Monoids with Central Idempotents (Edmond W. H. Lee) Portugaliae Mathematica (2011)

Let A denote the class of all aperiodic monoids with central idempotents. A description of all Cross subvarieties of A, based on identities that they satisfy and monoids that they cannot contain, is given. The ...

Finite Basis Problem for 2-Testable Monoids (Edmond W. H. Lee) Central European Journal of Mathematics (2011)

A monoid S 1 obtained by adjoining a unit element to a 2-testable semigroup S is said to be 2-testable. It is shown that a 2-testable monoid S 1 is either inherently non-finitely based or ...

Combinatorial Rees–Sushkevich Varieties That Are Cross, Finitely Generated, Or Small (Edmond W. H. Lee) Bulletin of the Australian Mathematical Society (2010)

A variety is said to be a Rees–Sushkevich variety if it is contained in a periodic variety generated by 0-simple semigroups. Recently, all combinatorial Rees–Sushkevich varieties have been shown to be finitely based. The present ...

On a Semigroup Variety of György Pollák (Edmond W. H. Lee) Novi Sad Journal of Mathematics (2010)

Let P be the variety of semigroups defined by the identity xyzx = x2. By a result of György Pollák, every subvariety of P is finitely based. The present article is concerned with subvarieties of ...

Finitely Generated Limit Varieties of Aperiodic Monoids with Central Idempotents (Edmond W. H. Lee) Journal of Algebra and Its Applications (2009)

A non-finitely based variety of algebras is said to be a limit variety if all its proper subvarieties are finitely based. Recently, Marcel Jackson published two examples of finitely generated limit varieties of aperiodic monoids ...

Hereditarily Finitely Based Monoids of Extensive Transformations (Edmond W. H. Lee) Algebra Universalis (2009)

It is shown that the monoid En of extensive transformations of a chain of order n is hereditarily finitely based if and only if n ≤ 3. It follows that the submonoid OEn of order-preserving ...

Lyndon's Groupoid Generates a Small Almost Cross Variety (Edmond W. H. Lee) Algebra Universalis (2009)

Lyndon’s groupoid of order seven is the first published example of a non-finitely based finite algebra. The main objective of the present article is to investigate the variety L generated by this groupoid and its ...

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