Mininjective rings

被引:123
作者
Nicholson, WK [1 ]
Yousif, MF [1 ]
机构
[1] OHIO STATE UNIV,DEPT MATH,LIMA,OH 45804
关键词
D O I
10.1006/jabr.1996.6796
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
A ring R is called right mininjective if every isomorphism between simple right ideals is given by left multiplication by an element of R. These rings are shown to be Morita invariant. If R is commutative it is shown that R is mininjective if and only if it has a squarefree socle, and that every image of R is mininjective if and only if R has a distributive lattice of ideals. If R is a semiperfect, right mininjective ring in which eR has nonzero right socle for each primitive idempotent e, it is shown that R admits a Nakayama permutation of its basic idempotents, and that its two socles are equal if every simple left ideal is an annihilator. This extends well known results on pseudo- and quasi-Frobenius rings. (C) 1997 Academic Press.
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收藏
页码:548 / 578
页数:31
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