Coherent rings and absolutely pure precovers

Guocheng Dai,Nanqing Ding

COMMUNICATIONS IN ALGEBRA(2019)

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摘要
In this article, we prove that a precovering class is closed under direct limits provided that is closed under direct products and pure submodules. As a corollary, we get that a ring R is left coherent if and only if the class of absolutely pure left R-modules is a precovering class.
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关键词
Absolutely pure module,coherent ring,direct limit,precovering class
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