2019/06/13 by Dandan Yang, Victoria Gould, Dandan, Yang +7 · 2 citations
Computer Science · Mathematics · #20M17 #20M30 #Advanced Algebra and Logic #FOS: Mathematics #Group Theory (math.GR) #Primary: 20M10 #Rings, Modules, and Algebras #Secondary: 20M12 #semigroups and automata theory
paper · doi:10.48550/arxiv.1906.05515
openalex publication_date 2019/06/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.