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.

Single-Authored Articles (43)

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 ...

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 counterintuitive since ...

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 ...

On the Variety Generated by Some Monoid of Order Five (Edmond W. H. Lee) Acta Scientiarum Mathematicarum (2008)

It is shown that the semigroup variety generated by the monoid A10=a, b : a2 = a, b2 = b, ba = 01 of order five is hereditarily finitely based and contains countably infinitely many ...

Combinatorial Rees–Sushkevich Varieties Are Finitely Based (Edmond W. H. Lee) International Journal of Algebra and Computation (2008)

A variety is said to be a Rees–Sushkevich variety if it is contained in a periodic variety generated by 0-simple semigroups. It is shown that all combinatorial Rees–Sushkevich varieties are finitely based.

Minimal Semigroups Generating Varieties with Complex Subvariety Lattices (Edmond W. H. Lee) International Journal of Algebra and Computation (2007)

A semigroup is complex if it generates a variety with the property that every finite lattice is embeddable in its subvariety lattice. In this paper, subvariety lattices of varieties generated by small semigroups will be ...

On a Simpler Basis for the Pseudovariety EDS (Edmond W. H. Lee) Semigroup Forum (2007)

A basis for the pseudovariety EDS which involves two distinct variables is computed. This improves upon a presently known basis for EDS that involves three distinct variables.

On Identity Bases of Exclusion Varieties for Monoids (Edmond W. H. Lee) Communications in Algebra (2007)

An exclusion variety is a variety that is maximal with respect to not containing some semigroup. It is shown that if the bases of all exclusion varieties for some periodic semigroup S are known, then ...

On the Complete Join of Permutative Combinatorial Rees–Sushkevich Varieties (Edmond W. H. Lee) International Journal of Algebra (2007)

A semigroup variety is a Rees–Sushkevich variety if it is contained in a periodic variety generated by 0-simple semigroups. The collection of all permutative combinatorial Rees–Sushkevich varieties constitutes an incomplete lattice that does not contain ...

Maximal Clifford Semigroups of Matrices (Edmond W. H. Lee) Sarajevo Journal of Mathematics (2006)

All maximal Clifford semigroups of matrices are identified up to isomorphism. If the ground field of the matrices is finite, then there exists a unique Clifford semigroup of maximum order.

Maximal Normal Orthogroups in Rings Containing No Infinite Semilattices (Edmond W. H. Lee) Communications in Algebra (2006)

Let R be a ring regarded as a multiplicative semigroup which contains no infinite subsemilattices. We investigate subsemigroups of R which are normal orthogroups, and present a construction from which all such maximal normal orthogroups ...

Subvarieties of the Variety Generated by the Five-Element Brandt Semigroup (Edmond W. H. Lee) International Journal of Algebra and Computation (2006)

All subvarieties of the variety B2 generated by the five-element Brandt semigroup are characterized. Based on this characterization, an algorithm is provided that decides if a finite set of identities defines, within B2, a finitely ...

Identity Bases for Some Non-exact Varieties (Edmond W. H. Lee) Semigroup Forum (2004)

Let A2 be the variety generated by the five-element non-orthodox 0-simple semigroup. This paper presents the identity bases for several subvarieties of A2 that are not generated by any completely 0-simple or completely simple semigroups. ...

Co-Authored Articles (18)

A survey on varieties generated by small semigroups and a companion website (João Araújo, João Pedro Araújo, Peter J. Cameron, et al.) Journal of Algebra (2023)

This paper presents new findings on varieties generated by small semigroups and groups, and offers a survey of existing results. A companion website is provided which hosts a computational system integrating automated reasoning tools, finite ...

The lattice of varieties of monoids (Sergey V. Gusev, Edmond W. H. Lee and Boris M. Vernikov) Japanese Journal of Mathematics (2022)

We survey results devoted to the lattice of varieties of monoids. Along with known results, some unpublished results are given with proofs. A number of open questions and problems are also formulated.

On join irreducible J-trivial semigroups (Edmond W. H. Lee, John Rhodes and Benjamin Steinberg) Rendiconti del Seminario Matematico della Università di Padova (2022)

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

Cancellable Elements of the Lattice of Monoid Varieties (Sergey V. Gusev and Edmond W. H. Lee) Acta Mathematica Hungarica (2021)

The set of all cancellable elements of the lattice of semigroup varieties has recently been shown to be countably infinite. But the description of all cancellable elements of the lattice MON of monoid varieties remains ...

Varieties of Monoids with Complex Lattices of Subvarieties (Sergey V. Gusev and Edmond W. H. Lee) Bulletin of the London Mathematical Society (2020)

A variety is finitely universal if its lattice of subvarieties contains an isomorphic copy of every finite lattice. Examples of finitely universal varieties of semigroups have been available since the early 1970s, but it is ...

Join irreducible semigroups (Edmond W. H. Lee, John Rhodes and Benjamin Steinberg) International Journal of Algebra and Computation (2019)

We begin a systematic study of finite semigroups that generate join irreducible members of the lattice of pseudovarieties of finite semigroups, which are important for the spectral theory of this lattice. Finite semigroups S that ...