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arXiv · 1906.05515

Coherency and constructions for monoids

Yang Dandan·Victoria Gould·Miklos Hartmann·Nik Ruskuc·Rida-E Zenab
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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.

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Yang Dandan, Victoria Gould, Miklos Hartmann, Nik Ruskuc, Rida-E Zenab. 2019-06-13. Coherency and constructions for monoids. https://arxiv.org/abs/1906.05515

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