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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.

Cominimaxness of local cohomology modules

Moharram Aghapournahr (2019)

Czechoslovak Mathematical Journal

Let R be a commutative Noetherian ring, I an ideal of R . Let t 0 be an integer and M an R -module such that Ext R i ( R / I , M ) is minimax for all i t + 1 . We prove that if H I i ( M ) is FD 1 (or weakly Laskerian) for all i < t , then the R -modules H I i ( M ) are I -cominimax for all i < t and Ext R i ( R / I , H I t ( M ) ) is minimax for i = 0 , 1 . Let N be a finitely generated R -module. We prove that Ext R j ( N , H I i ( M ) ) and Tor j R ( N , H I i ( M ) ) are I -cominimax for all i and j whenever M is minimax and H I i ( M ) is FD 1 (or weakly Laskerian) for all i .

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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