Extensions of generalized stable rings
Bull. Korean Math. Soc. 2009 Vol. 46, No. 6, 1091-1097
https://doi.org/10.4134/BKMS.2009.46.6.1091
Published online November 1, 2009
Zhang Wanru
HeXi University
Abstract : In this paper, we investigate the extensions of generalized stable rings. It is shown that a ring $R$ is a generalized stable ring if and only if $R$ has a complete orthogonal set $\{e_1,\ldots,e_n\}$ of idempotents such that $e_1Re_1,\ldots,e_nRe_n$ are generalized stable rings. Also, we prove that a ring $R$ is a generalized stable ring if and only if $R[[X]]$ is a generalized stable ring if and only if $T(R,M)$ is a generalized stable ring.
Keywords : generalized stable rings, complete orthogonal set of idempotents, ring extensions
MSC numbers : 16E50, 16U99
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