分次三角矩阵环的性质

分次三角矩阵环的性质

任艳丽¹, 王尧^1，2,3

1. 鞍山师范学院数学系, 鞍山 114005； 2. 吉林大学数学研究所，长春 130012；3. 南开大学数学学院，天津 300071

收稿日期:2003-03-17 修回日期:1900-01-01 出版日期:2003-10-26 发布日期:2003-10-26
通讯作者: 王尧

Properties of Graded Triangular Matrix Rings

REN Yan-li¹, WANG Yao^1,2,3

1. Department of Mathematics, Anshan Normal University, Anshan 114005, China; 2. College of Mathematics,Jilin University, Changchun 130012, China;3. College of Mathematics, Nankai Univeristy, Tianjin 300071, China

Received:2003-03-17 Revised:1900-01-01 Online:2003-10-26 Published:2003-10-26
Contact: WANG Yao

摘要/Abstract

摘要： 给定两个分次环R=_x∈MR_x, A= _x∈MA_x和一个分次双模V=_RV_A= _x∈MV_x, 可以得到一个分次三角矩阵环T. 对分次强π正则性、弱分次直有限性和与分次J根密切相关的几个分次环性质，讨论了T与R，A之间的性质关系.

关键词: 分次三角矩阵环, 分次强π正则性, 分次直有限性, 分次Jacobson根

Abstract: Given two graded rings R=_x∈MR_x, A=_x∈MA_x and one graded bimodule V=_RV_A= _x∈MV_x we can obtain a graded trigangular matrix ring T. In this paper are discussed the property relations among R,A and T for graded strongly π-regularity, weakly graded direct finiteness and some gr aded ring properties in close relationship with graded J-radical.

Key words: graded triangular matrix ring, graded strongly π-regu larity, graded direct finiteness, graded Jacobson radical

中图分类号:

O153.3

任艳丽, 王尧. 分次三角矩阵环的性质[J]. J4, 2003, 41(04): 458-462.

REN Yan-li, WANG Yao. Properties of Graded Triangular Matrix Rings[J]. J4, 2003, 41(04): 458-462.