ON THE FINITENESS OF FORMAL LOCAL COHOMOLOGY MODULES | ||
| Journal of Algebraic Systems | ||
| دوره 11، شماره 1، آذر 2023، صفحه 173-187 اصل مقاله (163.08 K) | ||
| نوع مقاله: Original Manuscript | ||
| شناسه دیجیتال (DOI): 10.22044/jas.2022.11072.1549 | ||
| نویسندگان | ||
| Shahram Rezaei* ؛ Mahbobeh Gasemi-Kalemasihi | ||
| Department of Mathematics, Payame Noor University (PNU), P.O. Box 19395- 4697, Tehran, Iran. | ||
| چکیده | ||
| Let a be an ideal of local ring (R;m) and M a nitely generated R-module. In this paper, we prove some results concerning niteness and minimaxness of formal local cohomology modules. In particular, we investigate some properties of top formal local cohomology FdimM=aM a (M) and we determine CosR(FdimM=aM a (M)), AnnR(FdimM=aM a (M)) and AttR(FdimM=aM a (M)). | ||
| کلیدواژهها | ||
| formal local cohomology؛ local cohomology؛ finiteness | ||
| مراجع | ||
|
1. M. Asgharzadeh and K. Divaani-Aazar, Finiteness properties of formal local cohomology modules and Cohen-Macaulayness, Comm. Algebra, 39 (2011), 1082–1103.
2. A. Atazadeh, M. Sedghi, R. Naghipour, On the annihilators and attached primes of top local cohomology modules, Archiv der Math., 102 (2014), 225–236.
3. M. H. Bijan-Zadeh, Sh. Rezaei, Artinianness and attached primes of formal local cohomology modules, Algebra Colloq., 21(2) (2014), 307–316.
4. M. Brodmann and R. Y. Sharp, Local cohomology: an algebraic introduction with geometric applications, Cambridge University Press, United Kingdom, 1998.
5. M. Eghbali, On Artinianness of formal local cohomology, colocalization and coassociated primes, Math. Scand., 113(1) (2013), 5–19.
6. I. G. MacDonald, Secondary representations of modules over a commutative ring, in Symposia Mat. 11, Istituto Nazionale di alta Matematica, Roma, (1973), 23–43.
7. H. Matsumura, Commutative ring theory, Cambridge University Press, 1986.
8. L. Melkersson, On asymptotic stability for sets of prime deals connected with the powers of an ideal, Math. Proc. Cambridge Philos. Soc., 107 (1990), 267–271.
9. L. Melkersson and P. Schenzel, The co-localization of an artinian module, Proc. Edinb. Math. Soc., 38 (1995), 121–131.
10. J. J. Rotman, An introduction to homological algebra, Academic Press, Orlando, 1979.
11. Sh. Rezaei, Minimaxness and finiteness properties of formal local cohomology modules, kodai Math. J., 38 (2015), 430–436.
12. P. Schenzel, On formal local cohomology and connectedness, J. Algebra, 315(2) (2007), 894–923.
13. S. Yassemi, Coassociated primes, Comm. Algebra, 23 (1995), 1473–1498.
14. H. Zöschinger, Minimax modules, J. Algebra, 102 (1986), 1–32.
15. H. Zöschinger, Über koassoziierte Primideale, Math. Scand., 63 (1988), 196– 211. | ||
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آمار تعداد مشاهده مقاله: 167 تعداد دریافت فایل اصل مقاله: 266 |
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