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Covers of Acts Over Monoids and Pure Epimorphisms

Published online by Cambridge University Press:  16 April 2014

Alex Bailey  and
James H. Renshaw
Alex Bailey
Affiliation:
Department of Mathematics, University of Southampton, Southampton SO17 1BJ, UK, ([email protected]; [email protected])
James H. Renshaw
Affiliation:
Department of Mathematics, University of Southampton, Southampton SO17 1BJ, UK, ([email protected]; [email protected])
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Abstract

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In 2001, Enochs's celebrated flat cover conjecture was finally proven, and the proofs (two different proofs were presented in the same paper) have since generated a great deal of interest among researchers. The results have been recast in a number of other categories and, in particular, for additive categories. In 2008, Mahmoudi and Renshaw considered a similar problem for acts over monoids but used a slightly different definition of cover. They proved that, in general, their definition was not equivalent to that of Enochs, except in the projective case, and left open a number of questions regarding the ‘other’ definition. This ‘other’ definition is the subject of the present paper and we attempt to emulate some of Enochs's work for the category of acts over monoids, and concentrate, in the main, on strongly flat acts. We hope to extend this work to other classes of acts, such as injective, torsion free, divisible and free, in a future report.

Keywords

monoidsactsstrongly flatcoverspure epimorphismscolimitsPrimary 20M50
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 57 , Issue 3 , October 2014 , pp. 589 - 617
Copyright
Copyright © Edinburgh Mathematical Society 2014 

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