幂零元幂等元个数有限的质环

幂零元幂等元个数有限的质环 PRIME RINGS WITH A FINITE NUMBER OF NILPOTENT AND IDEMPOTENT ELEMENTS 邱琦章 Qiu Qizhang 1 first-author 武汉大学数学系 武汉大学数学系 Department of mathematics, Wuhan University Department of mathematics, Wuhan University 幂零元在质环中起着重要作用。本文证明具有有限个（异于零的）幂零元的质环是有限环且与有限域上n阶全矩阵环同构。 In this paper the main result is Th. 1. Suppose R be a prime ring. The following conditions are equivalent ⅰ) RM n （F）, the total matrix ring over field F of degree n, where n≥2, F=GF（p m ）; ⅱ) R has a finite number of nilpotet elements4=0; ⅲ) R has a finite number of nilpotent elements which have index 2; ⅳ) R has a finite number of idempotent elements≠0, 1. 质环 有限环 全矩阵环 幂零元 幂等元 prime ring finite ring full matrix ring nilpotent element idempotent element 1991-02-01 2021-04-01 2