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arXiv · 1310.0742

A short note on strongly flat covers of acts over monoids

Alex Bailey·James Renshaw
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Abstract

Recently two different concepts of covers of acts over monoids have been studied. That based on coessential epimorphisms and that 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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Alex Bailey, James Renshaw. 2013-10-02. A short note on strongly flat covers of acts over monoids. https://arxiv.org/abs/1310.0742

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