相关于挠理论的(拟)连续模

(Quasi-)Continuous Modules Relative to the Torsion Theory

设M,N是R-Mod,τ=(T,F)是遗传挠理论,提出了模M是τ-N-(拟)连续模的概念,它是(拟)连续模的推广.给出了模M是τ-N-extending模的等价刻画,并对短正合序列0→N1→N→N2→0,证明了M是τ-N-(拟)连续模当且仅当M是τ-N1和τ-N2-(拟)连续模.

Let M,N be R-Mod,andτ=(T,F)be a hereditary torsion theory.In this paper,the concept that M as aτ-N-(quasi-)continuous module is introduced,which is a generalization of the(quasi-)continuous module,and some equivalent characterizations ofτ-N-extending module are given.Moreover,let 0→N1→N→N2→0 be an exact sequence,the paper proves that M is aτ-N-(quasi-)continuous module if and only if it is bothτ-N1-(quasi-)continuous andτ-N2-(quasi-)continuous.