Extensions of generalized stable rings
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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,…,e_n} of idempotents such that e_1Re_1,…, 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.
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,…,e_n} of idempotents such that e_1Re_1,…, 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.
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