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IPM
30
YEARS OLD

“School of Mathematics”

Paper   IPM / M / 15844
   School of Mathematics
  Title: Covering classes, strongly flat modules, and completions
  Author(s): Zahra Nazemian (JJoint with A. Facchini)
  Status: To Appear
  Journal: Math. Z.
  Supported by: IPM
  Abstract:
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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