Abstract

A monoid S is right coherent if every finitely generated subact of every finitely presented right S-act is finitely presented. This is a finiteness condition, and we investigate whether or not it is preserved under some standard algebraic and semigroup theoretic constructions: subsemigroups, homomorphic images, direct products, Rees matrix semigroups, including Brandt semigroups, and Bruck–Reilly extensions. We also investigate the relationship with the property of being weakly right noetherian, which requires all right ideals of S to be finitely generated.

中文翻译：

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词性的连贯性和构造

摘要

如果每个有限表示的正确S- act的每个有限生成的子行为都被有限表示，那么一个半群S是正确相干的。这是一个有限条件，我们研究它是否在某些标准的代数和半群理论构造下得以保留：亚半群，同态图像，直接乘积，Rees矩阵半群（包括Brandt半群）和Bruck-Reilly扩展。我们还研究了具有弱右Noetherian的性质的关系，这要求S的所有右理想都是有限生成的。