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Paper IPM / M / 15844  


Abstract:  
We study some closely interrelated notions of Homological Algebra: (1) We define a topology on modules over a notnecessarily commutative ring R that coincides with the Rtopology
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 Rtopology is a strongly flat Rmodule. (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 socalled 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 Rmodules are strongly flat.
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