EXTENSION AND TORSION FUNCTORS WITH RESPECT TO SERRE CLASSES

In this paper we generalize the Rigidity Theorem and Zero Divisor Conjecture for an arbitrary Serre subcategory of modules. For this purpose, for any regular M-sequence x 1 , ..., x n with respect to S we prove that if TorR2 ( R ( x 1 ,...,x n ) , M ) E S, then TorR i ( R ( x 1 ,...,x n ) , M ) E S, for all i >= 1 . Also we show that if Ext n +2 R ( R ( x 1 ,...,x n ) , M ) E S, then Exti R ( R ( x 1 ,...,x n ) , M ) E S, for all integers i >= 0 (i not equal n ) .