拟对偶双边模和对偶双边模

journal6 ›› 2002, Vol. 23 ›› Issue (4): 89-91.

拟对偶双边模和对偶双边模

（1.吉首大学数学与计算机科学系，湖南吉首 416000；2.吉首大学预科部，湖南吉首 416000)

出版日期:2002-12-15 发布日期:2012-11-09

Quasi-Dual Bimodules and Dual-Bimodules

(1.Department of Mathematics and Computer Science,Jishou University,Jishou 416000,Hunan China; 〗2.National Preparatory Department,Jishou University,Jishou 416000,Hunan China)

Online:2002-12-15 Published:2012-11-09
About author:LI Ai-hua(1971-),male,was born in Zhangjiajie,Hunan Province,lecturer of Dept. of Mathe. and Comp. Sci.,Jishou University,research area is algebra.

摘要/Abstract

摘要：拟对偶双边模SMR可以被刻画成MR的每一个本质子模K和S的所有本质左理想L分别满足rMlS(K)=K和lSrM(L)=L.拟对偶双边模和对偶双边模的关系表明：一个左拟对偶双边模SMR如果满足下列条件之一，则它成为坐对偶双边模：(1)SM 是单内射的并且MR是一个M-单内射kasch-模；（2）MR是一个M-单内射kasch-模并且对SS 的任意2个理想L1和L2 有rM(L1∩L2)=rM(L1)+rM(L2)；（3）SM是单内射的并且对MR的任意2个子模A和B，有lS(A∩B)=lS(A)+lS(B).

关键词： 拟对偶双边模, 对偶双边模, 零化子, M-单内射模

Abstract: A quasi-dual bimodule SMR can be characterized as every essential submodule K of MR and every essential left ideal L of S which satisfy rMlS(K)=K and lSrM(L)=L respectively.The relations are discussed between quasi-dual bimodules and dual-bimodules;a left quasi-dual bimodule is a left dual bimodule if it satisfies one of the following conditions:(ⅰ) SM is minimal injective and MR is a M-minimal injective kasch-module；(ⅱ) MR is a M-minimal injective kasch-module and rM(L1∩L2)=rM(L1)+rM(L2) for any two ideals L1 and L2 of SS;(ⅲ) SM is minimal injective and for any two submodules A and B of MR,lS(A∩B)=lS(A)+lS(B).

Key words: quasi-dual bimodules, dual-bimodules, annihilators, M-minimal-injective modules

李爱华, 张清良. 拟对偶双边模和对偶双边模[J]. journal6, 2002, 23(4): 89-91.

LI Ai-Hua, ZHANG Qing-Liang. Quasi-Dual Bimodules and Dual-Bimodules[J]. journal6, 2002, 23(4): 89-91.