关于一些自同态环为半完全环的模

On Certain Modules Whose Endomorphism Rings Are Semi-perfect

设M是有限生成的拟投射左R 模 ,那么End(RM )为半完全环的充要条件是M能分解成模直和 :M =M1 … Mr,其中每个End(RMi)为局部环 ;设R为整环 ,那么 ,对于任意有限生成的拟投射但非投射的R 模M ,End(RM )为半完全环的充要条件是R的Krull维数为 1和R的每个理想都有准素分解 ;设R为Dedekind整环 ,M是有限生成的扭R 模 ,那么End(RM )为半完全环 .

Let M be a finitely generated quasi projective R module but not projective, then End( RM) is semi perfect if and only if there is a direct decomposition of M such that M=M 1...M r , where each End( RM i) is a local ring. Let R be a commutative integral ring, then, for a finitely generated quasi projective R module M but not projective, End(M) is semi perfect if and only if the Krull dimension of R is 1 and each ideal of R has quasi primary decomposition. Let R be a Dedekind domain and M a finitely generated torsion R module, then End(R) is semi perfect.