Výsledky vyhledávání - "Vassilev, Janet C."

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Autor: Fouli, Louiza, Vassilev, Janet C., Vraciu, Adela-N.

Expanding on the work of Fouli and Vassilev \cite{FV}, we determine a formula for the *-$\rm{core}$ of an ideal in two different settings: (1) in a Cohen--Macaulay local ring of characteristic $p>0$, perfect residue field and test ideal of depth at l

Externí odkaz: http://arxiv.org/abs/0910.4597

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A look at the prime and semiprime operations of one-dimensional domains

Autor: Vassilev, Janet C.

We continue the analysis of prime and semiprime operations over one-dimensional domains started in \cite{Va}. We first show that there are no bounded semiprime operations on the set of fractional ideals of a one-dimensional domain. We then prove the

Externí odkaz: http://arxiv.org/abs/0905.1117

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Structure on the set of closure operations of a commutative ring

Autor: Vassilev, Janet C.

We investigate the algebraic structure on the set of closure operations of a ring. We show the set of closure operations is not a monoid under composition for a discrete valuation ring. Even the set of semiprime operations over a DVR is not a monoid;

Externí odkaz: http://arxiv.org/abs/0809.2021

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When is tight closure determined by the test ideal?

Autor: Vassilev, Janet C., Vraciu, Adela N.

We characterize the rings in which the equality $(\tau I:\tau)= I^*$ holds for every ideal $I \subset R$. Under certain assumptions, these rings must be either weakly F-regular or one-dimensional.

Externí odkaz: http://arxiv.org/abs/0809.1891

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Cofiniteness and associated primes of local cohomology modules

Autor: Marley, Thomas, Vassilev, Janet C.

Publikováno v: Journal of Algebra 256 (2002), 180-193

Let R be a regular local ring of dimension d, I an ideal of R, and M a finitely generated R-module of dimension n. We prove that the set of associated primes of Ext^i_R(R/I,H^j_I(M)) is finite for all i and j in the following cases: (1) dim M\le 3; (

Externí odkaz: http://arxiv.org/abs/math/0209216

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Local cohomology modules with infinite dimensional socles

Autor: Marley, Thomas, Vassilev, Janet C.

Publikováno v: Proc. American Math. Soc. 132 (2004), 3485-3490

Let T be a commutative Noetherian local ring of dimension at least two and R=T[x_1,...,x_n] a polynomial ring in n variables over T. Consider R as a graded ring with deg T = 0 and deg x_i = 1 for all i. Let I=R_+ and f a homogeneous polynomial whose

Externí odkaz: http://arxiv.org/abs/math/0209196

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