RD-flatness and RD-injectivity
Rings and Algebras
2014-02-18 v3
Abstract
It is proved that every commutative ring whose RD-injective modules are -RD-injective is the product of a pure semi-simple ring and a finite ring. A complete characterization of commutative rings for which each artinian (respectively simple) module is RD-injective, is given. These results can be obtained by using the properties of RD-flat modules and RD-coflat modules which are respectively the RD-relativization of flat modules and fp-injective modules. It is also shown that a commutative ring is perfect if and only if each RD-flat module is RD-projective.
Cite
@article{arxiv.math/0409551,
title = {RD-flatness and RD-injectivity},
author = {Francois Couchot},
journal= {arXiv preprint arXiv:math/0409551},
year = {2014}
}
Comments
A new section is added to the version published in Communications in Algebra where a complete proof of Theorem 3.1 is given