同调方程

Homological Equations

设Ｒ是左、右凝聚环，Ｒ~ωＲ是一个忠实平衡自正交双模．对有限表现左Ｒ－模Ａ和正整数ｎ，本文研究了形如， 的同调方程．给出了模范畴为有限表现右Ｒ-模｝是子模闭的充要条件，并举例说明了该模范畴并非总是子模闭的，

Let R be a left and right coherent ring and R~ωR a faithfully balanced selforthogonal bimodule. For any finitely presented left R-module A and a positive integer n, we study in this paper the homological equations such as A = EXt-R^n(X,ω). The necessary and sufficient conditions of the category of modules {EXt-R^n(B, R) | B is any finitely presented right R-module} being submodule closed are given, and some examples are given to explain that such a category of modules as above is not always submodule closed.