有限生成模自同态环的一种刻画

A characterization of endomorphism rings of finitely generated modules

定义了矩阵环的零化子,对有限生成模的自同态环进行了刻画.证明了有限生成左R-模的自同态环是环R上矩阵环的一个子环的同态像,并利用此结果给出了代数学中一些经典结论的新的证明.

It was defined annihilators of matrix rings and characterized endomorphism rings of finitely generated modules.The endomorphism ring of a finitely generated left R-module was proved to be the homomorphic image of a subring of the matrix ring over R,and a new proof to some classical results in algebra was given.