自同态环是NJ环的模及强NJ模的自同态环

Modules with NJ Endomorphism Ring and Endomorphism Rings of Strongly NJ Module

讨论了自同态环是NJ环的模以及强NJ模的自同态环.证明了abelian环上的投射模,若其自同态环是NJ环,则该模是强NJ模.通过例子说明了强NJ模的自同态环不一定是NJ环,证明了有限生成的强NJ模的自同态环是exchange环.证明了自同态环是NJ环的模,其直和项的自同态环也是NJ环.

The objec t of this paper is discussing the modules wi th NJ endomorphism r ing and endomor-phism rings of st rongly NJ module. It is proved that a project module on abel ian rings wi th NJ endomor-phism rings is st rongly NJ module. It is shown through examples that the endomorphism rings of st rongly NJ module is not necessari ly be NJ ring,and the endomorphism rings of fini te generated st rongly NJ module is exchange ring. It is proved that endomorphism ring is NJ rings module, the direct summand is also NJ en-domorphism ring.