On separation properties in semilattices.
Let We call a complex number “semigroup free“ if the semigroup generated by and is free and “free” if the group generated by and is free. First families of semigroup free ’s were described by J. L. Brenner, A. Charnow (1978). In this paper we enlarge the set of known semigroup free ’s. To do it, we use a new version of “Ping-Pong Lemma” for semigroups embeddable in groups. At the end we present most of the known results related to semigroup free and free numbers in a common picture....
We study the right regular representation of special Rees matrix semigroups over semigroups, and discuss their embedding in idempotent-free left simple semigroups.