| HOMOLOGICAL PROPERTIES OF TORSION CLASSES UNDER CHANGE OF RINGS |
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| 引用本文： | Yao Musheng. HOMOLOGICAL PROPERTIES OF TORSION CLASSES UNDER CHANGE OF RINGS[J]. 数学年刊B辑(英文版), 1994, 15(1): 1-8 |
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| 作者姓名： | Yao Musheng |
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| 摘 要： | ＨＯＭＯＬＯＧＩＣＡＬ ＰＲＯＰＥＲＴＩＥＳ ＯＦ ＴＯＲＳＩＯＮ ＣＬＡＳＳＥＳ ＵＮＤＥＲ ＣＨＡＮＧＥ ＯＦ ＲＩＮＧＳ ￥ＹＡＯＭＵＳＨＥＮＧＡｂｓｔｒａｃｔ：ＬｅｔＲｂｅａｒｉｎｇｗｉｔｈｉｄｅｎｔｉｔｙ，ｘｂｅａｃｅｎｔｒａｌｅｌｅｍｅｎ...
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| 关 键 词： | 环 陶森理论 一致性 中央基 |
| 收稿时间： | 1991-11-18 |
| 修稿时间： | 1992-01-03 |
HOMOLOGICAL PROPERTIES OF TORSION CLASSES UNDER CHANGE OF RINGS |
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| Yao Musheng. HOMOLOGICAL PROPERTIES OF TORSION CLASSES UNDER CHANGE OF RINGS[J]. Chinese Annals of Mathematics,Series B, 1994, 15(1): 1-8 |
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| Authors: | Yao Musheng |
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| Affiliation: | 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 quotientring of $R$ and $varphi :Rto R/xR$ 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 $R$-Modand torsion theories on $S$-Mod are investigated. Properties ofthe functor Ext$^n_R(N,-)$ are given. Properties of thelocalization functor $Q_{si}$are also investigated. |
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| Keywords: | Ring Torsion theory Module Homological proprties. |
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