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Full-Text Articles in Physical Sciences and Mathematics
Finite Basis Problem For 2-Testable Monoids, Edmond W. H. Lee
Finite Basis Problem For 2-Testable Monoids, Edmond W. H. Lee
Mathematics Faculty Articles
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 hereditarily finitely based, depending on whether or not the variety generated by the semigroup S contains the Brandt semigroup of order five. Consequently, it is decidable in quadratic time if a finite 2-testable monoid is finitely based.
On A Semigroup Variety Of György Pollák, Edmond W. H. Lee
On A Semigroup Variety Of György Pollák, Edmond W. H. Lee
Mathematics Faculty Articles
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 P and the lattice they constitute, where the main result is a characterization of finitely generated subvarieties of P. It is shown that a subvariety of P is finitely generated if and only if it contains finitely many subvarieties, and the identities defining these varieties are described. Specifically, it is decidable when a finite set of identities defines a finitely generated subvariety …
On The Complete Join Of Permutative Combinatorial Rees–Sushkevich Varieties, Edmond W. H. Lee
On The Complete Join Of Permutative Combinatorial Rees–Sushkevich Varieties, Edmond W. H. Lee
Mathematics Faculty Articles
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 the complete join J of all its varieties. The objective of this article is to investigate the subvarieties of J. It is shown that J is locally finite, non-finitely generated, and contains only finitely based subvarieties. The subvarieties of J are precisely the combinatorial Rees–Sushkevich varieties that do not contain a certain semigroup of order four.