Finitely based monoids

Abstract

We present a method for proving that a semigroup is finitely based and find some new sufficient conditions under which a monoid is finitely based. As an application, we find a class of finite monoids where the finite basis property behaves in a complicated way with respect to the lattice operations but can be recognized by a simple algorithm. The method results in a short proof of the theorem of E. Lee that every monoid that satisfies xtxysy = xtyxsy and xytxsy = yxtxsy is finitely based. Also, the method gives an alternative proof of the theorem of F. Blanchet-Sadri that a pseudovariety of n-testable languages is finitely based if and only if n < 4.

Published in Semigroup Forum

References in corpus (3)

• Finitely based sets of 2-limited block-2-simple words
• The Finite Basis Problem for Kiselman Monoids
• Non-finitely based monoids

Cited by in corpus (7)

• The finite basis problem for the monoid of 2 by 2 upper triangular tropical matrices
• Classification of limit varieties of J-trivial monoids
• Finitely based sets of 2-limited block-2-simple words
• The finite basis problem for words with at most two non-linear variables
• Limit varieties of monoids satisfying a certain identity
• The Finite Basis Problem for Kiselman Monoids
• Non-finitely based monoids