Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Covering classes, strongly flat modules, and completions   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 $ \mathcal{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 consider some results related to the question whether $
\mathcal{SF}$ a covering class implies $ \mathcal{SF}$ closed under direct
limit. This is a particular case of the so-called Enochs' Conjecture (whether
covering classes are closed under direct limit).
  Some of our results concerns 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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The categories of this paper are: plasm-ph
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The categories of this paper are: hep-lat
7
The categories of this paper are: hep-th
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The categories of this paper are: stat
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The categories of this paper are: chao-dyn
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The categories of this paper are: alg-geom
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The categories of this paper are: chem-ph
1
The categories of this paper are: cs
12
The categories of this paper are: nucl-th
4
The categories of this paper are: cond-mat
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The categories of this paper are: nlin
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The categories of this paper are: cmp-lg
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The categories of this paper are: math-ph
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The categories of this paper are: q-fin
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The categories of this paper are: q-alg
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The categories of this paper are: adap-org