On Diagonalization of Idempotent Matrices over APT Rings

作     者：郭学军 宋光天 GUO Xue-jun;SONG Guang-tian

作者机构：中国科学技术大学数学系安徽合肥230026 

出 版 物：《Journal of Mathematical Research and Exposition》 (数学研究与评论（英文版）)

年 卷 期：2001年第21卷第1期

页      面：21-26页

学科分类：07[理学] 070104[理学-应用数学] 0701[理学-数学] 070101[理学-基础数学] 

主　　题：Abelian ring APT ring idempotent matrix. 

摘      要：Let R be an abelian ring (all idempotents of R lie in the center of R), and A be an idempotent matrix over R. The following statements are proved: (a). A is equivalent to a diagonal matrix if and only if A is similar to a diagonal matrix. (b). If R is an APT (abelian projectively trivial) ring, then A can be uniquely diagonalized as diag{el, ..., en} and ei divides ei+1. (c). R is an APT ring if and only if R/I is an APT ring, where I is a nilpotent ideal of R. By (a), we prove that a separative abelian regular ring is an APT ring.