Coherency and constructions for monoids
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 semi-groups, 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.
Citation
Dandan , Y , Gould , V , Hartmann , M , Ruskuc , N & Zenab , R-E 2020 , ' Coherency and constructions for monoids ' , Quarterly Journal of Mathematics , vol. 71 , no. 4 , pp. 1461-1488 . https://doi.org/10.1093/qmath/haaa040
Publication
Quarterly Journal of Mathematics
Status
Peer reviewed
ISSN
0033-5606Type
Journal article
Description
Funding: UK Engineering and Physical Sciences Research Council (EPSRC) grant EP/I032312/1. Research also partially supported by the Hungarian Scientific Research Fund (OTKA) grant PD115705. The research of Yang Dandan was supported by grant 20170604 of the Young Talents Project of Shaanxi Association for Science and Technology, by grants 20103176174 and JB180714 of the Fundamental Research Funds for the Central Universities, and by grant 2020JM-178 of Shaanxi Province Basic Research Program of Natural Science.Collections
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