Document Type : Original Manuscript


Department of Mathematics, Payame Noor University (PNU), P.O. Box 19395- 4697, Tehran, Iran.


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 x1; :::; xn with respect to S we prove that if TorR 2 ((x1;:::;x R n); M) 2 S, then
TorR i ((x1;:::;x R n); M) 2 S, for all i ≥ 1. Also we show that if Extn R+2((x1;:::;x R n); M) 2 S,
then Exti R((x1;:::;x R n); M) 2 S, for all integers i ≥ 0 (i ̸= n).


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