半群的完美性

Pub Date : 2023-02-01 DOI:10.1017/S0013091523000159

V. Laan, Alvin Lepik

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摘要

如果酉右范畴中的每个对象都作用在半群上，则我们称半群为右完全半群。本文将关于右完全半群的结果推广到半群的情况。在我们的主要定理中，我们将给出等价于可因子分解半群的右完全性的九个条件。我们还证明了右完全性是可因子分解半群的Morita不变量。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Perfection for semigroups

Abstract 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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