Semigroup varieties with a small number of term operations

Abstract

We give an equational characterization of (varieties of) semigroups having a pn-sequence bounded above by a polynomial function of n. This is achieved by studying the syntactical connections between certain semigroup identities and their equational consequences.

On free spectra of finite completely regular semigroups and monoids

“…An important invariant closely related to f n (A) is the p n -sequence of A, p n (A), which counts the number of those n-ary term operations (operations on A induced by well-formed terms in the signature of A) which are essential, that is, which depend on all variables featured in the underlying term. For an overview of the general theory of free spectra and p n -sequences we refer to [3], while for some of the results concerning p n -sequences of semigroups the reader is directed to consult [4][5][6][7][8][9][10] and the references listed in those papers.…”