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A short note on strongly flat covers of acts over monoids

A short note on strongly flat covers of acts over monoids
A short note on strongly flat covers of acts over monoids
Recently two different concepts of covers of acts over monoids have been studied by a number of authors and many interesting results discovered. One of these concepts is based on coessential epimorphisms and the other is based on Enochs' definition of a flat cover of a module over a ring. Two recent papers have suggested that in the former case, strongly flat covers are not unique. We show that these examples are in fact false and so the question of uniqueness appears to still remain open. In the latter case, we re-present an example due to Kruml that demonstrates that, unlike the case for flat covers of modules, strongly flat covers of S-acts do not always exist.
0037-1912
416-422
Bailey, Alex
cd2762de-6a67-4ffc-ab42-2842ca378fa8
Renshaw, James
350100c1-f7c7-44d3-acfb-29b94f21731c
Bailey, Alex
cd2762de-6a67-4ffc-ab42-2842ca378fa8
Renshaw, James
350100c1-f7c7-44d3-acfb-29b94f21731c

Bailey, Alex and Renshaw, James (2016) A short note on strongly flat covers of acts over monoids. Semigroup Forum, 93 (2), 416-422. (doi:10.1007/s00233-016-9784-y).

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Abstract

Recently two different concepts of covers of acts over monoids have been studied by a number of authors and many interesting results discovered. One of these concepts is based on coessential epimorphisms and the other is based on Enochs' definition of a flat cover of a module over a ring. Two recent papers have suggested that in the former case, strongly flat covers are not unique. We show that these examples are in fact false and so the question of uniqueness appears to still remain open. In the latter case, we re-present an example due to Kruml that demonstrates that, unlike the case for flat covers of modules, strongly flat covers of S-acts do not always exist.

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e-pub ahead of print date: 21 July 2016
Published date: 16 September 2016
Organisations: Pure Mathematics

Identifiers

Local EPrints ID: 358818
URI: https://eprints.soton.ac.uk/id/eprint/358818
ISSN: 0037-1912
PURE UUID: 22395afc-29ab-4788-a267-6b5ebd3ed70d
ORCID for James Renshaw: ORCID iD orcid.org/0000-0002-5571-8007

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Date deposited: 14 Oct 2013 13:24
Last modified: 27 Jul 2019 00:38

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