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| HOMOLOGICAL PROPERTIES OF TORSION CLASSES UNDER CHANGE OF RINGS |
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Citation： |
Yao Musheng.HOMOLOGICAL PROPERTIES OF TORSION CLASSES UNDER CHANGE OF RINGS[J].Chinese Annals of Mathematics B,1994,15(1):1~8 |
| Page view： 1023
Net amount： 779 |
Authors： |
Yao Musheng; |
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| Abstract： |
Let $R$ be a ring with identity, $x$ be a central element of $R$
which is neither a unit nor a zero divisor. $S=R/xR$ is the quotient
ring of $R$ and $\varphi :R\to R/xR$ is the natural map.
$R$-Mod\, (resp.
$S$-Mod) denotes the category of unital left $R$-modules(resp. $S$-modules).
In this paper, relationships betwee torsion theories on $R$-Mod
and torsion theories on $S$-Mod are investigated. Properties of
the functor Ext$^n_R(N,-)$ are given. Properties of the
localization functor $Q_{\si}$are also investigated. |
Keywords： |
Ring, Torsion theory, Module, Homological proprties |
Classification： |
16E30 |
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