Coherency and constructions for monoids

Y. Dandan; V. Gould; M. Hartmann; Nik Ruskuc; R-E. Zenab

doi:10.1093/qmath/haaa040

Coherency and constructions for monoids

Y. Dandan, V. Gould, M. Hartmann, Nik Ruskuc, R-E. Zenab

Research output: Contribution to journal › Article › peer-review

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.

Original language	English
Pages (from-to)	1461-1488
Number of pages	28
Journal	Quarterly Journal of Mathematics
Volume	71
Issue number	4
Early online date	11 Dec 2020
DOIs	https://doi.org/10.1093/qmath/haaa040
Publication status	Published - Dec 2020

Keywords

Monoid
S-act
Coherency
Regular
Finitary properties

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10.1093/qmath/haaa040

coherencyrevised
Copyright © 2020 the Author(s). Published by Oxford University Press. All rights reserved. This work has been made available online in accordance with publisher policies or with permission. Permission for further reuse of this content should be sought from the publisher or the rights holder. This is the author created accepted manuscript following peer review and may differ slightly from the final published version. The final published version of this work is available at https://doi.org/10.1093/qmath/haaa040.
Accepted author manuscript, 388 KBLicence: Unspecified

Cite this

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title = "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.",

keywords = "Monoid, S-act, Coherency, Regular, Finitary properties",

author = "Y. Dandan and V. Gould and M. Hartmann and Nik Ruskuc and R-E. Zenab",

note = "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.",

year = "2020",

month = dec,

doi = "10.1093/qmath/haaa040",

language = "English",

volume = "71",

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issn = "0033-5606",

publisher = "Oxford University Press",

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TY - JOUR

T1 - Coherency and constructions for monoids

AU - Dandan, Y.

AU - Gould, V.

AU - Hartmann, M.

AU - Ruskuc, Nik

AU - Zenab, R-E.

N1 - 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.

PY - 2020/12

Y1 - 2020/12

N2 - 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.

AB - 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.

KW - Monoid

KW - S-act

KW - Coherency

KW - Regular

KW - Finitary properties

UR - https://arxiv.org/abs/1906.05515

U2 - 10.1093/qmath/haaa040

DO - 10.1093/qmath/haaa040

M3 - Article

SN - 0033-5606

VL - 71

SP - 1461

EP - 1488

JO - Quarterly Journal of Mathematics

JF - Quarterly Journal of Mathematics

IS - 4

ER -

Coherency and constructions for monoids

Abstract

Keywords

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