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3-dimensional sundials

Enrico Carlini, Maria Catalisano, Anthony Geramita (2011)

Open Mathematics

R. Hartshorne and A. Hirschowitz proved that a generic collection of lines on ℙn, n≥3, has bipolynomial Hilbert function. We extend this result to a specialization of the collection of generic lines, by considering a union of lines and 3-dimensional sundials (i.e., a union of schemes obtained by degenerating pairs of skew lines).

A functorial approach to the behaviour of multidimensional control systems

Jean-François Pommaret, Alban Quadrat (2003)

International Journal of Applied Mathematics and Computer Science

We show how to use the extension and torsion functors in order to compute the torsion submodule of a differential module associated with a multidimensional control system. In particular, we show that the concept of the weak primeness of matrices corresponds to the torsion-freeness of a certain module.

A Generalization of Baer's Lemma

Molly Dunkum (2009)

Czechoslovak Mathematical Journal

There is a classical result known as Baer’s Lemma that states that an R -module E is injective if it is injective for R . This means that if a map from a submodule of R , that is, from a left ideal L of R to E can always be extended to R , then a map to E from a submodule A of any R -module B can be extended to B ; in other words, E is injective. In this paper, we generalize this result to the category q ω consisting of the representations of an infinite line quiver. This generalization of Baer’s Lemma...

A generalization of the finiteness problem of the local cohomology modules

Ahmad Abbasi, Hajar Roshan-Shekalgourabi (2014)

Czechoslovak Mathematical Journal

Let R be a commutative Noetherian ring and 𝔞 an ideal of R . We introduce the concept of 𝔞 -weakly Laskerian R -modules, and we show that if M is an 𝔞 -weakly Laskerian R -module and s is a non-negative integer such that Ext R j ( R / 𝔞 , H 𝔞 i ( M ) ) is 𝔞 -weakly Laskerian for all i < s and all j , then for any 𝔞 -weakly Laskerian submodule X of H 𝔞 s ( M ) , the R -module Hom R ( R / 𝔞 , H 𝔞 s ( M ) / X ) is 𝔞 -weakly Laskerian. In particular, the set of associated primes of H 𝔞 s ( M ) / X is finite. As a consequence, it follows that if M is a finitely generated R -module and N is an 𝔞 -weakly...

A new version of Local-Global Principle for annihilations of local cohomology modules

K. Khashyarmanesh, M. Yassi, A. Abbasi (2004)

Colloquium Mathematicae

Let R be a commutative Noetherian ring. Let and be ideals of R and let N be a finitely generated R-module. We introduce a generalization of the -finiteness dimension of f ( N ) relative to in the context of generalized local cohomology modules as f ( M , N ) : = i n f i 0 | ( 0 : R H i ( M , N ) ) , where M is an R-module. We also show that f ( N ) f ( M , N ) for any R-module M. This yields a new version of the Local-Global Principle for annihilation of local cohomology modules. Moreover, we obtain a generalization of the Faltings Lemma.

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