关于齐次完全可约模的结构

关于齐次完全可约模的结构 ON THE STRUCTURE OF HOMOGENEOUS COMPLETELY REDUCIBLE MODULES 吴泉水 Wu Quanshui 1 first-author 复旦大学数学系 研究生 复旦大学数学系 研究生 本文在[1]的基础上进一步讨论齐次完全可约模与除环上的向量空间之间的关系。我们将证明:（一）任一齐次完全可约U-模M可看成一除环K上的向量空间,并且,如果P表示M的中心化子,则M作为左P-模的中心化子Ω与它的某一K-子空间M 0 的线性变换完全环一致;（二）Ω中元作为左P-模M的自同态的秩与它作为K-向量空间M 0 的线性变换的秩相等;（三）M作为左P-模的子模格与M 0 的K-子模格同构。 In this paper we obtain the following results following[1]: （ⅰ） Any homogeneous completely reducible U-module M can be viewed as a vector space over some division ring K. Moreover, let P be the centralizer of M, then the centrlier Ω of M as left P-module is the same as the complete ring of linear transformations of a K-vector subspace M s of M. （ⅱ） The rank of an element in Ω as an endomorphism of left P-module M is epual to the rank of it as a linear transformation of K-vector space M s . （ⅲ） There is a one to one order preserving correspondence between the submodules of M（inclusion of set） as left P-module and the K-subvector spaces of M s . We also give some simpler proofs of several theorems in[1] and generalize some results in it. 1986-01-01 2021-04-01 1