منابع مشابه
Deformation of F-purity and F-regularity
For a Noetherian local domain (R, m, K), it is an open question whether strong F–regularity deforms. We provide an affirmative answer to this question when the canonical module satisfies certain additional assumptions. The techniques used here involve passing to a Gorenstein ring, using an anti– canonical cover.
متن کاملFailure of F-purity and F-regularity in Certain Rings of Invariants
Let Fq be a finite field of characteristic p, K a field containing it, and R = K[X1, . . . , Xn] a polynomial ring in n variables. The general linear group GLn(Fq) has natural action on R by degree preserving ring automorphisms. L. E. Dickson showed that the subring of elements which are fixed by this group action is a polynomial ring, [Di], though for an arbitrary subgroupG of GLn(Fq), the str...
متن کاملSurjectivity of multiplication and F -regularity of multigraded rings
Let R be a noetherian Z-graded integral domain. Then the subset Σ(R) := {λ ∈ Z | Rλ 6= 0} is a finitely generated subsemigroup of Z. We say that R is surjectively graded if for any λ, μ ∈ Σ(R), the product Rλ⊗R0 Rμ → Rλ+μ is surjective. This is essentially a generalization of the degree-one generation property of N-graded rings. The purpose of this paper is to study this property, mainly for no...
متن کاملF-regularity relative to modules
In this paper we will generalize some of known results on the tight closure of an ideal to the tight closure of an ideal relative to a module .
متن کاملGeneralized f-clean rings
In this paper, we introduce the new notion of n-f-clean rings as a generalization of f-clean rings. Next, we investigate some properties of such rings. We prove that $M_n(R)$ is n-f-clean for any n-f-clean ring R. We also, get a condition under which the denitions of n-cleanness and n-f-cleanness are equivalent.
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ژورنال
عنوان ژورنال: Journal of Algebra
سال: 1995
ISSN: 0021-8693
DOI: 10.1006/jabr.1995.1071