Small varieties of finite semigroups and extensions
Jean-Éric Pin, Howard Straubing, Denis Thérien · Journal of the Australian Mathematical Society Series A Pure Mathematics and Statistics · 1984
Abstract We find the atoms of certain subclasses of varieties of finite semigroups and the corresponding varieties of languages. For example we give a new description of languages whose syntactic monoids are R-trivial and idempotent. We also describe the least variety containing all commutative semigroups and at least one non-commutative semigroup. Finally we extend to varieties of finite semigroups some classical results about semilattice decomposition of semigroups.