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Another version of cosupport in D ( R )

Junquan Qin, Xiao Yan Yang (2023)

Czechoslovak Mathematical Journal

The goal of the article is to develop a theory dual to that of support in the derived category D ( R ) . This is done by introducing ‘big’ and ‘small’ cosupport for complexes that are different from the cosupport in D. J. Benson, S. B. Iyengar, H. Krause (2012). We give some properties for cosupport that are similar, or rather dual, to those of support for complexes, study some relations between ‘big’ and ‘small’ cosupport and give some comparisons of support and cosupport. Finally, we investigate the...

Cofiniteness and finiteness of local cohomology modules over regular local rings

Jafar A'zami, Naser Pourreza (2017)

Czechoslovak Mathematical Journal

Let ( R , 𝔪 ) be a commutative Noetherian regular local ring of dimension d and I be a proper ideal of R such that mAss R ( R / I ) = Assh R ( I ) . It is shown that the R -module H I ht ( I ) ( R ) is I -cofinite if and only if cd ( I , R ) = ht ( I ) . Also we present a sufficient condition under which this condition the R -module H I i ( R ) is finitely generated if and only if it vanishes.

Cofiniteness of torsion functors of cofinite modules

Reza Naghipour, Kamal Bahmanpour, Imaneh Khalili Gorji (2014)

Colloquium Mathematicae

Let R be a Noetherian ring and I an ideal of R. Let M be an I-cofinite and N a finitely generated R-module. It is shown that the R-modules T o r i R ( N , M ) are I-cofinite for all i ≥ 0 whenever dim Supp(M) ≤ 1 or dim Supp(N) ≤ 2. This immediately implies that if I has dimension one (i.e., dim R/I = 1) then the R-modules T o r i R ( N , H I j ( M ) ) are I-cofinite for all i,j ≥ 0. Also, we prove that if R is local, then the R-modules T o r i R ( N , M ) are I-weakly cofinite for all i ≥ 0 whenever dim Supp(M) ≤ 2 or dim Supp(N) ≤ 3. Finally, it is shown that...

Cohen-Macaulayness of multiplication rings and modules

R. Naghipour, H. Zakeri, N. Zamani (2003)

Colloquium Mathematicae

Let R be a commutative multiplication ring and let N be a non-zero finitely generated multiplication R-module. We characterize certain prime submodules of N. Also, we show that N is Cohen-Macaulay whenever R is Noetherian.

Construction of a controller with a generalized linear immersion

Javier Diaz-Vargas, Dennis Tuyub-Puc, Celia Villanueva-Novelo (2011)

Kybernetika

Gröbner bases for modules are used to calculate a generalized linear immersion for a plant whose solutions to its regulation equations are polynomials or pseudo-polynomials. After calculating the generalized linear immersion, we build the controller which gives the robust regulation.

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