On regularity of the center of the endomorphism ring of an Abelian group

Karpenko, A. V.; Misyakov, V. M.

doi:10.1007/s10958-008-9186-0

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“…A semigroup S is called idempotent or band if xx = x for all x ∈ S. See for examples in [4,7] A semigroup S is called endo-regular if its monoid of endomorphisms is regular. The regularity of the endomorphism monoid for groups were studied by several authors (see for examples [1,5]). In particular, Theorem 1.2 in [6] gives a characterization of regular endomorphisms on groups.…”

Section: Introductionmentioning

confidence: 99%

Endomorphisms of Clifford semigroups with injective structure homomorphisms

Worawiset¹,

Koppitz²

2020

ADM

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In the present paper, we study semigroups of endomorphisms on Clifford semigroups with injective structure homomorphisms, where the semilattice has a least element. We describe such Clifford semigroups having a regular endomorphism monoid. If the endomorphism monoid on the Clifford semigroup is completely regular then the corresponding semilattice has at most two elements. We characterize all Clifford semigroups Gα∪Gβ (α>β) with an injective structure homomorphism, where Gα has no proper subgroup, such that the endomorphism monoid is completely regular. In particular, we consider the case that the structure homomorphism is bijective.

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Section: Introductionmentioning

confidence: 99%