EXTENSION AND TORSION FUNCTORS WITH RESPECT TO SERRE CLASSES | ||
| Journal of Algebraic Systems | ||
| دوره 11، شماره 2، فروردین 2024، صفحه 113-123 اصل مقاله (157.8 K) | ||
| نوع مقاله: Original Manuscript | ||
| شناسه دیجیتال (DOI): 10.22044/jas.2022.11683.1597 | ||
| نویسندگان | ||
| Sajad Arda؛ Seadat ollah Faramarzi* | ||
| Department of Mathematics, Payame Noor University (PNU), P.O. Box 19395- 4697, Tehran, Iran. | ||
| چکیده | ||
| 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). | ||
| کلیدواژهها | ||
| Serre classes؛ Zero Divisor Conjecture؛ RigidityTheorem؛ Top local cohomology | ||
| مراجع | ||
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1. M. Asgharzadeh and M. Tousi, Cohen Macaulayness with respect to serre classes, Illinois J. Math., 53 (2009), 67–85.
2. M. Auslander, Modules over unramified regular local rings, Illinois J. Math., 5 (1961), 631–647.
3. K. Bahmanpour, A complex of modules and its applications to local cohomology and extension functors, Math. Scand., 117 (2015), 150–160.
4. W. Bruns and J. Herzog, Chen-Macaulay Rings, Cambridge University Press, Cambridge, 1998.
5. S. Lichtenbaum, On the vanishing of Tor in regular local rings, Illinois J. Math., 10 (1966), 220–236.
6. C. Peskin and L. Szpiro, Dimension projective finie et cohomologie locale, Inst. Hautes tudes Sci. Publ. Math., 42 (1973), 47–119.
7. J. Rotman, An Introduction to Homological Algebra, Springer, New York, 2009. | ||
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