Semiperfect finitely generated abelian semigroups without involution

Finitely Generated Abelian Groups

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...

MATH 436 Notes: Finitely generated Abelian groups

Definition 1.1 (Direct Products). Let {Gα}α∈I be a collection of groups indexed by an index set I. We may form the Cartesian product ∏ α∈I Gα. The elements of this Cartesian product can be denoted by tuples (aα)α∈I . We refer to the entry aα as the αth component of this tuple. We define a multiplication on this Cartesian product componentwise, i.e., (aα) ⋆ (bα) = (aα ⋆α bα) where ⋆α is the grou...

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.