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Covers of acts over monoids II

Covers of acts over monoids II
Covers of acts over monoids II
In 1981 Edgar Enochs conjectured that every module has a
at cover
and finally proved this, independently with Bican and El Bashir, in 2001.
Enochs had in fact considered different types of covers as early as 1963,
for example injective and torsion free covers, and since then a great deal
of effort has been spent on their study. In 2008, Mahmoudi and Renshaw
initiated the study of
at covers of acts over monoids but their definition
of cover was slightly different from that of Enochs. Recently, Bailey and
Renshaw produced some preliminary results on the `other' type of cover
and it is this work that is extended in this paper. We consider free,
divisible, torsion free and injective covers and demonstrate that in some
cases the results are quite different from the module case.
0037-1912
257-274
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 (2013) Covers of acts over monoids II. Semigroup Forum, 87 (1), 257-274. (doi:10.1007/s00233-013-9469-8).

Record type: Article

Abstract

In 1981 Edgar Enochs conjectured that every module has a
at cover
and finally proved this, independently with Bican and El Bashir, in 2001.
Enochs had in fact considered different types of covers as early as 1963,
for example injective and torsion free covers, and since then a great deal
of effort has been spent on their study. In 2008, Mahmoudi and Renshaw
initiated the study of
at covers of acts over monoids but their definition
of cover was slightly different from that of Enochs. Recently, Bailey and
Renshaw produced some preliminary results on the `other' type of cover
and it is this work that is extended in this paper. We consider free,
divisible, torsion free and injective covers and demonstrate that in some
cases the results are quite different from the module case.

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More information

Submitted date: 30 June 2012
Accepted/In Press date: December 2012
Published date: 21 June 2013
Organisations: Pure Mathematics

Identifiers

Local EPrints ID: 341047
URI: https://eprints.soton.ac.uk/id/eprint/341047
ISSN: 0037-1912
PURE UUID: 7f30a561-1148-48c0-8346-c1b17e2c6028
ORCID for James Renshaw: ORCID iD orcid.org/0000-0002-5571-8007

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Date deposited: 12 Jul 2012 08:29
Last modified: 27 Jul 2019 00:38

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Contributors

Author: Alex Bailey
Author: James Renshaw ORCID iD

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