Free monoids are coherent

V Gould; M Hartmann; Nik Ruskuc

doi:10.1017/S0013091516000079

Free monoids are coherent

V Gould, M Hartmann, Nik Ruskuc

School of Mathematics and Statistics

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

Abstract

A monoid S is said to be right coherent if every finitely generated subact of
every finitely presented right S-act is finitely presented. Left coherency is defined dually and S is coherent if it is both right and left coherent. These notions are analogous to those for a ring R (where, of course, S-acts are replaced by R-modules). Choo, Lam and Luft have shown that free rings are coherent. In this note we prove that, correspondingly, any free monoid is coherent, thus answering a question posed by the first author in 1992.

Original language	English
Pages (from-to)	127-131
Number of pages	5
Journal	Proceedings of the Edinburgh Mathematical Society
Volume	60
Issue number	1
Early online date	15 Jun 2016
DOIs	https://doi.org/10.1017/S0013091516000079
Publication status	Published - Feb 2017

Keywords

Free monoids
S-acts
Coherency

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10.1017/S0013091516000079

gouldhartmannruskuccoherency1_4
© 2015, Edinburgh Mathematical Society. This work is made available online in accordance with the publisher’s policies. This is the author created, accepted version manuscript following peer review and may differ slightly from the final published version. The final published version of this work is available at journals.cambridge.org / https://dx.doi.org/10.1017/S0013091516000079
Accepted author manuscript, 240 KB

Theory of Semigroups: Representation theory of Semigroups
Ruskuc, N. (PI)
EPSRC
1/04/12 → 30/09/15
Project: Standard

Cite this

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Free monoids are coherent

Abstract

Keywords

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Theory of Semigroups: Representation theory of Semigroups

Cite this