分次非奇异三角矩阵环  

Graded nonsingular triangular matrix rings

作　　者：王尧[1] 任艳丽[2] 

机构地区：[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

出　　处：《吉林大学学报（理学版）》2004年第4期503-507,共5页Journal of Jilin University:Science Edition

基　　金：国家自然科学基金(批准号:102710176).

摘　　要：设Ω是一个适合左(右)消去律的Monoid,S= x∈ΩSx和T= x∈ΩTx是两个有1的Ω分次环,B=SBT= x∈ΩBx是一个Ω分次(S,T)双模,R=SB0T= x∈ΩSxBx0Tx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,BT是分次非奇异模.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=SB 0T=x∈ΩS_xB_x 0T_x 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 nonsingular module.

关 键 词：非奇异环 分次三角矩阵环 非奇异模 分次环 消去律 忠实模 证明 BT 双模 

分 类 号：O153.3[理学—数学] O151[理学—基础数学]