DS环的Morita invariant性

MORITA INVARIANT PROPERTIES OF DS RINGS

证明了关于左 DS环的几个结果 :1 )若对 R的中心幂等元 e,有 e Re和 (1 -e) R(1 -e)都是左 DS环 ,则 R是左 DS环 ;2 ) R是左 DS环当且仅当全矩阵环 Mn(R)是左 DS环 ;3 )左 DS环是 Moritainvariant;4) R是左 DS环当且仅当 R是左 MC2环且极小内射左 R-模的同态像是极小内射左 R-模 .

Some results of left DS rings are given: 1) If for a central idempotent e of a ring R with eRe and (1-e)R(1-e) are all left DS rings, then R is left DS ring; 2) R is left DS ring iff full matrix rings M n(R) is left DS ring; 3) Left DS rings are Morita invariant; 4) R is left DS ring iff R is left MC2 ring and every homomorphism images of minijective left R modules is minijective modules.