%0 Journal Article
%T Finitely based monoids
%A Olga Sapir
%J Mathematics
%D 2014
%I arXiv
%R 10.1007/s00233-015-9709-1
%X 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.
%U http://arxiv.org/abs/1402.5136v6