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| Paper IPM / M / 15844 |
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| Abstract: | |
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We study some closely interrelated notions of Homological Algebra: (1) We define a topology on modules over a not-necessarily commutative ring R that coincides with the R-topology
defined by
Matlis when R is commutative. (2) We consider the class SF of strongly flat modules when R is a right Ore domain with classical right quotient ring Q. Strongly flat modules are flat. The completion of R in its R-topology is a strongly flat R-module. (3) We prove some results related to the question whether
SF a covering class implies SF closed under direct limits.
This is a particular case of the so-called Enochs' Conjecture (whether covering classes are closed
under direct limits).
Some of our results concern right chain domains. For instance, we show
that if the class of strongly flat modules over a right chain domain R is
covering, then
R is right invariant. In this case, flat R-modules are strongly flat.
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