形式三角矩阵环上模的若干注记

Some Notes of Modules over Formal Triangular Matrix Rings

设T是一个形式三角矩阵环,其中A,B是环且M是左B-右A-双模。利用环模理论和同调代数的方法,研究了形式三角矩阵环T上模的有限生成性、投射性以及FG-投射性等性质及其刻画。证明了右T-模(X⊕Y)T、右B-模YB、右A-模XA关于其子模f(YM)的商模之间具有一定的相关性,补充了形式三角矩阵环上模的基础理论。

Let T be a formal triangular matrix ring, where A , B are rings and M is a left B- right A- bimodules. By using methods of rings and modules and homological algebra, some properties and characerizations of modules over ring T are main investigated, including finitely generated property, projective property and FG- projective property. And prove that there is pertinence between right T -module (X⊕Y) T , the factor module of right A -module A modulo its submodule f(Y?M), and right B -module Y B. This complements the basic theory of modules over formal triangular matrix rings.