On maximal pseudo-varieties of finite monoids and semigroups
The main result of the article states that there are no elements in the lattice of semigroup pseudo-varieties covered by the pseudo-variety of all finite semigroups. The author shows that a slight modification of the proof permits to obtain the analogous result for pseudo-varieties of monoids. He notes also that methods of the paper can be used to prove that some proper pseudo-varieties of semigroups do not have maximal subpseudo-varieties. This is proved explicitly for the pseudo-variety of all finite semigroups all whose subgroups are commutative. One can note that recently \textit{S. Margolis, M. Sapir} and \textit{P. Weil} have proved that each of the three pseudo-varieties mentioned above is not decomposable into the join of two proper subpseudo-varieties [Rapports LITP 96/01 (1996)]. Clearly, this implies the results of the paper under review.
scientific article; zbMATH DE number 862280