强极大TAF代数的交不可约D-模

MEET IRREDUCIBLE D-MODULES IN STRONGLY MAXIMAL TAF ALGEBRAS

本文研究了强极大TAF代数的交不可约D-模的有关性质.利用矩阵单元链的方法,证明了全上三角矩阵代数中任一D-模等于包含它的所有交不可约D-模的交,建立了强极大TAF代数的交不可约D-模与矩阵单元链之间的对应关系,推广了强极大TAF代数中关于理想的若干性质.

In this article, we consider the properties of meet irreducible D-Modules in strongly maximal TAF algebras. Using the method of the chain of matrix units, we prove that any D-module in full triangular matrix algebras is equal to the intersection of meet irreducible D-Modules which contain it. And at the same time the corresponding relation between meet irreducible D-modules and the chain of matrix units is established, which extends the properties about ideals in strongly maximal TAF algebras.