منابع مشابه
Innnitely Many Associated Primes of Frobenius Powers and Local Cohomology
A modiication of Katzman's example is given to produce a two-generated ideal in a two-dimensional Noetherian integral domain for which the set of associated primes of all the Frobenius powers is innnite. A further modiication yields a four-dimensional Noetherian integral domain and a ve-dimensional Noetherian local integral domain for which an explicit second local cohomology module has innnite...
متن کاملInfinitely many associated primes of Frobenius powers and local cohomology
A modification of Katzman’s example is given to produce a two-generated ideal in a two-dimensional Noetherian integral domain for which the set of associated primes of all the Frobenius powers is infinite. A further modification yields a four-dimensional Noetherian integral domain and a five-dimensional Noetherian local integral domain for which an explicit second local cohomology module has in...
متن کاملAssociated primes of local cohomology modules and of Frobenius powers
We construct normal hypersurfaces whose local cohomology modules have infinitely many associated primes. These include unique factorization domains of characteristic zero with rational singularities, as well as F-regular unique factorization domains of positive characteristic. As a consequence, we answer a question on the associated primes of Frobenius powers of ideals, which arose from the loc...
متن کاملEmbedded Associated Primes of Powers of Square-free Monomial Ideals
An ideal I in a Noetherian ringR is normally torsion-free if Ass(R/I) = Ass(R/I) for all t ≥ 1. We develop a technique to inductively study normally torsion-free square-free monomial ideals. In particular, we show that if a squarefree monomial ideal I is minimally not normally torsion-free then the least power t such that I has embedded primes is bigger than β1, where β1 is the monomial grade o...
متن کاملAssociated primes of local cohomology modules and Frobenius powers
We construct normal hypersurfaces whose local cohomology modules have infinitely many associated primes. These include hypersurfaces of characteristic zero with rational singularities, as well as F-regular hypersurfaces of positive characteristic. As a consequence, we answer a question on the associated primes of certain families of ideals which arose from the localization problem in tight clos...
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ژورنال
عنوان ژورنال: Journal of Pure and Applied Algebra
سال: 2019
ISSN: 0022-4049
DOI: 10.1016/j.jpaa.2019.02.020