Semigroups With a Dense Subgroup

Unary Semigroups with an Associate Subgroup

Dense Subsets in Semigroups

This article covers a theory of dense subsets in general semigroups, including basic algebraic properties of dense and disjunctive subsets, characterizations of dense subset preserving homomorphisms and some remarkable properties of dense elements.

Semigroups of real functions with dense orbits

Let FI = {f : I → I| f(x) = (Ax + B)/(Cx + D); AD − BC 6= 0}, where I is an interval. For x ∈ I, let Ωx be the orbit of x under the action of the semigroup of functions generated by f, g ∈ FI . Our main result in this paper is to describe all f, g ∈ FI such that Ωx is dense in I for all x.

Semigroups of matrices with dense orbits

We prove that for any n ≥ 1 there exist n × n matrices A and B such that for any vector x ∈ R with a nonzero first component, the orbit of x under the action of the semigroup generated by A and B is dense in R. As a corollary, we prove that for a large set of diagonal matrices A and B and any vector V with nonzero entries, the orbit of any vector under the semigroup generated by the affine maps...

Homomorphisms and Congruences of Medial Semigroups with an Associate Subgroup

Let S be the model of a semigroup with an associate subgroup whose identity is a medial idempotent constructed by Blyth and Martins considered as a unary semigroup. For another such semigroup T , we construct all unary homomorphisms of S into T in terms of their parameters. On S we construct all unary congruences again directly from its parameters. This construction leads to a characterization ...