N-Semigroups and their translation semigroups

Abstract

AbstractIfhis a homomorphism of anN-semigroup onto anN-semigroupS′, thenhinduces a homomorphismhof the translation semigroup Λ(S) ofSinto Λ(S′) ofS′. We will study the relations between the structures ofS,S′ and Λ(S), Λ(S)′, and will introduce the specialized concepts ofN-semigroupsS. In particular, we will be interested in power-joined steady or endlessN-semigroups. Finally, we will consider admissibility of torsion abelian groups, that is, consider what torsion abelian group can be a structure group of a power-joined steadyN-semigroup.