Stable Rings for Morita Contexts of Generalized Power Series Rings
Received:January 08, 2007  Revised:July 13, 2007
Key Word: Morita Context   unit 1-stable range   generalized power series.
Fund ProjectL:the Natural Science Foundation of Hunan Province (No.06jj20053); the Scientific Research Fund of Hunan Provincial Education Department (Nos.06A017; 07C268).
 Author Name Affiliation OUYANG Lun Qun Department of Mathematics, Hunan Science and Technology University, Hunan 411201, China Department of Mathematics, Hunan Normal University, Hunan 410081, China
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In this paper, we show that if rings $A$ and $B$ are $(s,2)$-rings, then so is the ring of a Morita Context $([[A^{S,\leq}]], [[B^{S,\leq}]],[[M^{S,\leq}]],[[N^{S,\leq}]],\psi^{S},\phi^{S})$ of generalized power series. Also we get analogous results for unit 1-stable ranges, $GM$-rings and rings which have stable range one. These give new classes of rings satisfying such stable range conditions.