Semigroups with finitely generated universal left congruence

Finitely Generated Weakly Reductive Commutative Semigroups∗

We give characterizations of the property of being weakly reductive for finitely generated commutative semigroups. As a consequence of these characterizations we obtain an algorithm for determining from a presentation of a finitely generated commutative semigroup whether it is weakly reductive. Furthermore, we present some connections between cancellative finitely generated commutative semigrou...

Ring With All Finitely Generated Modules Retractable

Injectives in Finitely Generated Universal Horn Classes

Let K be a finite set of finite structures. We give a syntactic characterization of the property: every element of K is invective in ISP(K). We use this result to establish that 4 is invective in ISP(s) for every two-element algebra i. ?0. Introduction. Let K be a finite set of finite structures for a first-order language. In this paper we give a syntactic characterization (Theorem 4) of the pr...

An Invariant Measure for Finitely Generated Rational Semigroups

For a nitely generated rational semigroup G we establish the existence of a probability measure = G on the Julia set J(G) which has a certain invariance property with respect to the semigroup.

Finitary Power Semigroups of Infinite Groups Are Not Finitely Generated

For a semigroup S the finitary power semigroup of S, denoted Pf (S), consists of all finite subsets of S under the usual multiplication. The main result of this paper asserts that Pf (G) is not finitely generated for any infinite group G.