Semigroups strongly Morita equivalent to monoids

Lepik, Alvin

doi:10.1007/s10998-021-00427-5

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Morita Invariance1

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2023

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“…Clearly, groups are perfect semigroups. Factorizable semigroups Morita equivalent to a given group are precisely Rees matrix semigroups over that group [19].…”

Section: Morita Invariancementioning

confidence: 99%

Perfection for semigroups

Laan¹,

Lepik²

2023

Proceedings of the Edinburgh Mathematical Society

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We call a semigroup right perfect if every object in the category of unitary right acts over that semigroup has a projective cover. In this paper, we generalize results about right perfect monoids to the case of semigroups. In our main theorem, we will give nine conditions equivalent to right perfectness of a factorizable semigroup. We also prove that right perfectness is a Morita invariant for factorizable semigroups.

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“…Clearly, groups are perfect semigroups. Factorizable semigroups Morita equivalent to a given group are precisely Rees matrix semigroups over that group [19].…”

Section: Morita Invariancementioning

confidence: 99%