On finitely related semigroups.
Let \(\mathbf A=\langle A,F\rangle\) be an algebra, where \(A\) is a set and \(F\) is a set of finitary operations on \(A\). The algebra \(\mathbf A\) is called finitely related if there exist subalgebras \(R_1,\dots,R_l\) of finitary powers of \(\mathbf A\) such that every operation on \(A\) that preserves every \(R_i\) (\(1\leq i\leq l\)) is a term operation on \(A\). Finitely related algebras were considered by many authors under varied names. It is shown that the following finite semigroups are finitely related: commutative semigroups, 3-nilpotent monoids, regular bands, semigroups with a single idempotent, and Clifford semigroups. Some examples of not finitely related semigroups are presented, particularly, the 6-element Brandt monoid is not finitely related. Some open problems are formulated.
scientific article; zbMATH DE number 6176161
scientific article