Document Type : Original Manuscript


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



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
a (M) and we determine CosR(FdimM=aM
a (M)), AnnR(FdimM=aM
a (M)) and
a (M)).


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.