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On some free semigroups, generated by matrices

Piotr Słanina (2015)

Czechoslovak Mathematical Journal

Let A = 1 2 0 1 , B λ = 1 0 λ 1 . We call a complex number λ “semigroup free“ if the semigroup generated by A and B λ is free and “free” if the group generated by A and B λ is free. First families of semigroup free λ ’s were described by J. L. Brenner, A. Charnow (1978). In this paper we enlarge the set of known semigroup free λ ’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....

On special Rees matrix semigroups over semigroups

Attila Nagy, Csaba Tóth (2023)

Commentationes Mathematicae Universitatis Carolinae

We study the right regular representation of special Rees matrix semigroups over semigroups, and discuss their embedding in idempotent-free left simple semigroups.

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