分次非奇异三角矩阵环

分次非奇异三角矩阵环

王尧^1,2，任艳丽²

1. 南开大学数学科学学院，天津 300071； 2. 鞍山师范学院数学系, 鞍山 114005

收稿日期:2004-02-24 修回日期:1900-01-01 出版日期:2004-10-26 发布日期:2004-10-26
通讯作者: 王尧

Graded nonsingular triangular matrix rings

WANG Yao^1,2, REN Yan-li²

1. School of Mathematical, Nankai University, Tianjin 300071, China; 2. Department of Mathematics, Anshan Normal University, Anshan 114005, China

Received:2004-02-24 Revised:1900-01-01 Online:2004-10-26 Published:2004-10-26
Contact: WANG Yao

摘要/Abstract

摘要： 设Ω是一个适合左（右）消去律的Monoid, S=_x∈ΩS_x和T =_x∈ΩT_x是两个有1的Ω分次环， B=_SB_T=_x∈ΩB_x是一个Ω分次（S，T）双模， R是由它们确定的Ω分次三角矩阵环. 证明了当_SB是分次忠实模时, R是分次非奇异环当且仅当T是分次非奇异环, B_T是分次非奇异模.

关键词: 分次三角矩阵环, 分次本质子模, 分次非奇异环, 分次非奇异模

Abstract: Let Ω be a multiplicative left(right) cancellative monoid, S=_x∈ΩS_x and T=_x∈ΩT_x be two Ω-graded rings with 1, and B=_SB_T=_{x∈ΩB_x be a Ω-graded (S,T)-bimodule, R is the graded triangular matrix ring determined by S,T and _SB_T. It is shown that if _SB is graded faithful then R is a graded nonsingular ring if and only if T is a graded nonsingular ring and B_T is a graded nonsin gular module.}

Key words: graded triangular matrix ring, graded essential submodule, graded nonsingular ring, graded nonsingular module

中图分类号:

O153.3

王尧，任艳丽. 分次非奇异三角矩阵环[J]. J4, 2004, 42(04): 503-507.

WANG Yao, REN Yan-li. Graded nonsingular triangular matrix rings[J]. J4, 2004, 42(04): 503-507.