TY - JOUR ID - 2734 TI - EXTENSION AND TORSION FUNCTORS WITH RESPECT TO SERRE CLASSES JO - Journal of Algebraic Systems JA - JAS LA - en SN - 2345-5128 AU - Arda, Sajad AU - Faramarzi, Seadat ollah AD - Department of Mathematics, Payame Noor University (PNU), P.O. Box 19395- 4697, Tehran, Iran. Y1 - 2024 PY - 2024 VL - 11 IS - 2 SP - 113 EP - 123 KW - Serre classes KW - Zero Divisor Conjecture KW - RigidityTheorem KW - Top local cohomology DO - 10.22044/jas.2022.11683.1597 N2 - 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 ΜΈ= n). UR - https://jas.shahroodut.ac.ir/article_2734.html L1 - https://jas.shahroodut.ac.ir/article_2734_a44138a7e8e87779437d5827a091c18b.pdf ER -