On generalized stable rings |
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| Authors: | Huanyin Chen |
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| Affiliation: | Department of Mathematics , Hunan Normal University , Changsha, 410006, P.R.China E-mail: chyzxl@sparc2.hunnu.edu.cn |
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| Abstract: | In this paper, we introduce the class of generalized stable rings and investigate equivalent characterizations of such rings. We show that EndR R is a generalized stable ring if and only if any right H-module decompositions M = A 1 + B 1 = A 2 + B 2 with A 1 ? A ? A 2 implies that there exist C,D,E ≤ M such that M = C + D B 1 = c + E + B 2 with.C ? A. Also we show that every generalized stable ring is a GE-ring and matrices over generalized stable regular ring can be diagonalized by some weakly invertible matrices. |
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| Keywords: | generalized stable ring GE-ring regularity |
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