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A ring R has weakly stable range one provided that aR +bR = R implies that there exists ay 2 R such that a + by 2 R is rightor left invertible. We prove, in this paper, that every regular elementin an exchange ring having weakly stable range one is the sum of anidempotent and a weak unit. This generalize the corresponding result ofone-sided unit-regular ring. Extensions of power comparability and powercancellation are also studied.1. IntroductionA ring R is said to be an exchange ring if for every rightR-module A andany two decompositionsA = M N =Li2 I Ai, whereMR = RR and I is anite index set, there exist submodulesA0i Ai such thatA = M (Li2 I A0i).It is well known that regular rings,-regular rings, unitC-algebras of realrank zero, semiperfect rings, left or right continuous rings and clean rings areall exchange rings. For general theory of exchange rings, we refer the readersto [10]. Following Wei and Tong (cf. [11]), a ringR is said to have weakly
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참고문헌 (11)
참고문헌 신청
/ 1997 / Comparability of modules over regular rings 25 (11) : 3531 ~ 3543
/ 1997 / Elements in one-sided unit regular rings 25 (8) : 2517 ~ 2529
/ 1999 / Exchange rings with artinian primitive factors 2 (2) : 201 ~ 207
/ 2000 / Power-substitution, exchange rings and unit -regularity 28 (11) : 5223 ~ 5233
/ 2001 / A characterization of unit regular rings 29 (5) : 2293 ~ 2295
/ 1997 / Elements in one-sided unit regular rings 25 (8) : 2517 ~ 2529
/ 1999 / Exchange rings with artinian primitive factors 2 (2) : 201 ~ 207
/ 2000 / Power-substitution, exchange rings and unit -regularity 28 (11) : 5223 ~ 5233
/ 2001 / A characterization of unit regular rings 29 (5) : 2293 ~ 2295
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