EXTENSION AND TORSION FUNCTORS WITH RESPECT TO SERRE CLASSES
نویسندگان
1 Department of Mathematics, Payame Noor University (PNU), P.O. Box 19395- 4697, Tehran, Iran.
2 Department of Mathematics, Payame Noor University (PNU), P.O. Box 19395- 4697, Tehran, Iran.
doi
10.22044/jas.2022.11683.1597چکیده
In this paper we generalize the Rigidity Theorem and Zero Divisor Conjecture for an arbitrary Serre subcategory of modules. For this purpose, for any regularM-sequence x1; :::; xn with respect to S we prove that if TorR 2 ((x1;:::;x R n); M) 2 S, thenTorR 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).
