منابع مشابه
The Upper Nilradical and Jacobson Radical of Semigroup Graded Rings
Given a semigroup S, we prove that if the upper nilradical Nil∗(R) is homogeneous whenever R is an S-graded ring, then the semigroup S must be cancelative and torsion-free. In case S is commutative the converse is true. Analogs of these results are established for other radicals and ideals. We also describe a large class of semigroups S with the property that whenever R is a Jacobson radical ri...
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Let Q be an affine semigroup generating Z, and fix a finitely generated Z -graded module M over the semigroup algebra k[Q] for a field k. We provide an algorithm to compute a minimal Z-graded injective resolution of M up to any desired cohomological degree. As an application, we derive an algorithm computing the local cohomology modulesH I(M) supported on any monomial (that is, Z -graded) ideal...
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The Goto number of a parameter ideal Q in a Noetherian local ring (R, m) is the largest integer q such that Q : m is integral over Q. The Goto numbers of the monomial parameter ideals of R = k[[x1 , x2 , . . . , xν ]] are characterized using the semigroup of R. This helps in computing them for classes of numerical semigroup rings, as well as on a case by case basis. The minimal Goto number of R...
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Let G be a finite group and R a strongly G-graded ring. The question of when R is semisimple (meaning in this paper semisimple artinian) has been studied by several authors. The most classical result is Maschke’s Theorem for group rings. For crossed products over fields there is a satisfactory answer given by Aljadeff and Robinson [3]. Another partial answer for skew group rings was given by Al...
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ژورنال
عنوان ژورنال: Journal of Algebra and Its Applications
سال: 2015
ISSN: 0219-4988,1793-6829
DOI: 10.1142/s0219498815501029