Note on residually finite rings
Note on residually finite rings
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关于剩余有限环的注意事项
DOI：
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发表时间：
2000
期刊：
影响因子：
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通讯作者：
C. Faith
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文献类型：
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作者：
C. Faith
本文讨论了Varadarajan[93]和[98/99]引入的剩余有限（= RF）模和环。具体来说，有几个定理可以简化证明并推广Varadarajan的一些结果，即。定理1。在M有限的情况下，RF右r模是有限层状的（=），它有有限本质函数。Corollay。如果T是一个右RF值有有限个简单的右R模，那么R是有限的。定理2。如果每个局部环Rm在极大理想m处是有限的，则交换环R是剩余有限的。
This paper is on the subject of residually finite (= RF) modules and rings introduced by Varadarajan [93] and [98/99]. Specifically there are several theorems that simplify proofs and generalize some results of Varadarajan, namely. Theorem 1. An RF right R-module is finitely bedded (= has finite essential socle iff M is finite. Corollay. If T is a right RF woth just finitely many simple ringht R-modules, them R is fimite. Theorem 2. A commutative ring R is residually finite iff every local ring Rm at a maximal ideal m is finite.