Gamma semigroup whose gamma acts are quasi–injective
Mehdi Sadiq Abbas, Saad Abdulkadhim Al-Saadi, Abdulqader Faris · Journal of Discrete Mathematical Sciences and Cryptography · 2024
In this paper, we interpose the notion tools, Noetherian gamma acts, and γ – idempotent elements, to describe gamma semigroups in which all gamma acts are quasi – injective. We get the following equivalent (i) a gamma semigroup S is Noetherian and each finite direct sum of quasi – injective SΓ-act is quasi – injective (ii) direct sum of quasi – injective SΓ-act is quasi – injective. Also we prove that an γ – monoid is ΓRQI if and only if all right Γ- ideal generated by γ – idempotent element.