liu.seSearch for publications in DiVA
Change search
Link to record
Permanent link

Direct link
BETA
Melkersson, Leif
Publications (10 of 10) Show all publications
Aghapournahr, M. & Melkersson, L. (2014). Artinianness of local cohomology modules. Arkiv för matematik, 52(1), 1-10
Open this publication in new window or tab >>Artinianness of local cohomology modules
2014 (English)In: Arkiv för matematik, ISSN 0004-2080, E-ISSN 1871-2487, Vol. 52, no 1, p. 1-10Article in journal (Refereed) Published
Abstract [en]

Some uniform theorems on the artinianness of certain local cohomology modules are proven in a general situation. They generalize and imply previous results about the artinianness of some special local cohomology modules in the graded case.

Place, publisher, year, edition, pages
Royal Swedish Academy of Sciences, Institut Mittag-Leffler, 2014
National Category
Natural Sciences
Identifiers
urn:nbn:se:liu:diva-105895 (URN)10.1007/s11512-013-0187-y (DOI)000332797200001 ()
Available from: 2014-04-14 Created: 2014-04-12 Last updated: 2017-12-05
Melkersson, L. (2012). Cofiniteness with respect to ideals of dimension one. Journal of Algebra, 372, 459-462
Open this publication in new window or tab >>Cofiniteness with respect to ideals of dimension one
2012 (English)In: Journal of Algebra, ISSN 0021-8693, E-ISSN 1090-266X, Vol. 372, p. 459-462Article in journal (Refereed) Published
Abstract [en]

We prove that the category of modules cofinite with respect to an ideal of dimension one in a noetherian ring is a full abelian subcategory of the category of modules. The proof is based on a criterion for cofiniteness with respect to an ideal of dimension one. Namely for such ideals it suffices that the two first Ext-modules in the definition for cofiniteness are finitely generated. This criterion is also used to prove very simply that all local cohomology modules of a finitely generated module with respect to an ideal of dimension one in an arbitrary noetherian ring are cofinite with respect to the ideal.

Place, publisher, year, edition, pages
Elsevier, 2012
Keywords
Cofinite module, Local cohomology module
National Category
Engineering and Technology
Identifiers
urn:nbn:se:liu:diva-86368 (URN)10.1016/j.jalgebra.2012.10.005 (DOI)000311187200023 ()
Available from: 2012-12-14 Created: 2012-12-14 Last updated: 2017-12-06
Aghapournahr, M. & Melkersson, L. (2010). A natural map in local cohomology. ARKIV FOR MATEMATIK, 48(2), 243-251
Open this publication in new window or tab >>A natural map in local cohomology
2010 (English)In: ARKIV FOR MATEMATIK, ISSN 0004-2080, Vol. 48, no 2, p. 243-251Article in journal (Refereed) Published
Abstract [en]

Let R be a Noetherian ring, a an ideal of R, M an R-module and n a non-negative integer. In this paper we first study the finiteness properties of the kernel and the cokernel of the natural map f: Ext(R)(n) (R/alpha, M) -andgt; Hom(R)(R/alpha, H-alpha(n) (M)), under some conditions on the previous local cohomology modules. Then we get some corollaries about the associated primes and Artinianness of local cohomology modules. Finally we will study the asymptotic behavior of the kernel and the cokernel of the natural map in the graded case.

Place, publisher, year, edition, pages
Springer Science and Business Media, 2010
National Category
Mathematics
Identifiers
urn:nbn:se:liu:diva-58658 (URN)10.1007/s11512-009-0115-3 (DOI)000280594800003 ()
Available from: 2010-08-22 Created: 2010-08-20 Last updated: 2010-08-22
Aghapournahr, M. & Melkersson, L. (2010). Finiteness properties of minimax and coatomic local cohomology modules. ARCHIV DER MATHEMATIK, 94(6), 519-528
Open this publication in new window or tab >>Finiteness properties of minimax and coatomic local cohomology modules
2010 (English)In: ARCHIV DER MATHEMATIK, ISSN 0003-889X, Vol. 94, no 6, p. 519-528Article in journal (Refereed) Published
Abstract [en]

Let R be a noetherian ring, alpha an ideal of R, and M an R-module. We prove that for a finite module M, if H-alpha(i)(M) is minimax for all i andgt;= r andgt;= 1, then H-alpha(i)(M) is artinian for i andgt;= r. A local-global principle for minimax local cohomology modules is shown. If H-alpha(i)(M) is coatomic for i andlt;= r (M finite) then H-alpha(i)(M) is finite for i andlt;= r. We give conditions for a module which is locally minimax to be a minimax module. A non-vanishing theorem and some vanishing theorems are proved for local cohomology modules.

Place, publisher, year, edition, pages
Springer Science Business Media, 2010
Keywords
Local cohomology, Minimax module, Coatomic module
National Category
Mathematics
Identifiers
urn:nbn:se:liu:diva-57419 (URN)10.1007/s00013-010-0127-z (DOI)000278347200003 ()
Available from: 2010-06-18 Created: 2010-06-18 Last updated: 2010-06-18
Aghapournahr, M. & Melkersson, L. (2009). COFINITENESS AND COASSOCIATED PRIMES OF LOCAL COHOMOLOGY MODULES. Mathematica Scandinavica, 105(2), 161-170
Open this publication in new window or tab >>COFINITENESS AND COASSOCIATED PRIMES OF LOCAL COHOMOLOGY MODULES
2009 (English)In: Mathematica Scandinavica, ISSN 0025-5521, E-ISSN 1903-1807, Vol. 105, no 2, p. 161-170Article in journal (Refereed) Published
Abstract [en]

Let R be a noetherian ring, alpha an ideal of R such that dim R/alpha = 1 and M a finite R-module. We will study cofiniteness and some other properties of the local cohomology modules H-alpha(i)(M). For an arbitrary ideal alpha and an R-module M (not necessarily finite), we will characterize alpha-cofinite artinian local cohomology modules. Certain sets of coassociated primes of top local cohomology modules over local rings are characterized.

National Category
Mathematics
Identifiers
urn:nbn:se:liu:diva-52888 (URN)
Available from: 2010-01-13 Created: 2010-01-12 Last updated: 2017-12-12
Aghapournahr, M. & Melkersson, L. (2008). Local cohomology and Serre subcategories. Journal of Algebra, 320(3), 1275-1287
Open this publication in new window or tab >>Local cohomology and Serre subcategories
2008 (English)In: Journal of Algebra, ISSN 0021-8693, E-ISSN 1090-266X, Vol. 320, no 3, p. 1275-1287Article in journal (Refereed) Published
Abstract [en]

The membership of the local cohomology modules H-a(n) (M) of a module M in certain Serre subcategories of the category of modules is studied from below (i < n) and from above (i > n). Generalizations of depth and regular sequences are defined. The relation of these notions to local cohomology are found. It is shown that the membership of the local cohomology modules of a finite module in a Serre subcategory in the upper range just depends on the support of the module. (C) 2008 Elsevier Inc. All rights reserved.

Keywords
local cohomology, Serre subcategory, S-regular sequences, S-depth
National Category
Engineering and Technology
Identifiers
urn:nbn:se:liu:diva-45879 (URN)10.1016/j.jalgebra.2008.04.002 (DOI)
Available from: 2009-10-11 Created: 2009-10-11 Last updated: 2017-12-13
Melkersson, L. (2005). Modules cofinite with respect to an ideal. Journal of Algebra, 285(2), 649-668
Open this publication in new window or tab >>Modules cofinite with respect to an ideal
2005 (English)In: Journal of Algebra, ISSN 0021-8693, E-ISSN 1090-266X, Vol. 285, no 2, p. 649-668Article in journal (Refereed) Published
Abstract [en]

[No abstract available]

National Category
Mathematics
Identifiers
urn:nbn:se:liu:diva-24712 (URN)10.1016/j.jalgebra.2004.08.037 (DOI)6958 (Local ID)6958 (Archive number)6958 (OAI)
Available from: 2009-10-07 Created: 2009-10-07 Last updated: 2017-12-13
Melkersson, L. (2004). Problems and results on cofiniteness: A survey. In: Homological methods on commutative algebra,2002 (pp. 69). Tehran, Iran: IPM Information Center
Open this publication in new window or tab >>Problems and results on cofiniteness: A survey
2004 (English)In: Homological methods on commutative algebra,2002, Tehran, Iran: IPM Information Center , 2004, p. 69-Conference paper, Published paper (Refereed)
Place, publisher, year, edition, pages
Tehran, Iran: IPM Information Center, 2004
National Category
Mathematics
Identifiers
urn:nbn:se:liu:diva-24711 (URN)6957 (Local ID)6957 (Archive number)6957 (OAI)
Available from: 2009-10-07 Created: 2009-10-07
Melkersson, L. (2003). Modules cofinite with respect to an ideal. Linköping: Linköpings universitet
Open this publication in new window or tab >>Modules cofinite with respect to an ideal
2003 (English)Report (Other academic)
Place, publisher, year, edition, pages
Linköping: Linköpings universitet, 2003
National Category
Mathematics
Identifiers
urn:nbn:se:liu:diva-22423 (URN)LiTH-MAT-R (ISRN)1638 (Local ID)1638 (Archive number)1638 (OAI)
Available from: 2009-10-07 Created: 2009-10-07
Melkersson, L. (2003). Problems and results on cofiniteness: A Survey. Linköping: Linköpings universitet
Open this publication in new window or tab >>Problems and results on cofiniteness: A Survey
2003 (English)Report (Other academic)
Place, publisher, year, edition, pages
Linköping: Linköpings universitet, 2003
National Category
Mathematics
Identifiers
urn:nbn:se:liu:diva-22769 (URN)LiTH-MAT-R (ISRN)2094 (Local ID)2094 (Archive number)2094 (OAI)
Available from: 2009-10-07 Created: 2009-10-07
Organisations

Search in DiVA

Show all publications