Note on residually finite rings |
| |
| Authors: | Carl Faith |
| |
| Affiliation: | 1. Dept. of Mathematics , Rutgers The State University , Busch Campus, Hill Center 110 Frelinghuysen Road, Piscataway, N.J, 08854-8019 E-mail: cfaithOmath.rutgers.edu;2. 199 Longview Ave, Princeton, NJ, 08540Current addresscarlfaithfiaol.com |
| |
| Abstract: | 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. |
| |
| Keywords: | |
|
|
