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Laskerian lattices

C. Jayaram (2003)

Czechoslovak Mathematical Journal

In this paper we investigate prime divisors, B w -primes and z s -primes in C -lattices. Using them some new characterizations are given for compactly packed lattices. Next, we study Noetherian lattices and Laskerian lattices and characterize Laskerian lattices in terms of compactly packed lattices.

Linear gradings of polynomial algebras

Piotr Jędrzejewicz (2008)

Open Mathematics

Let k be a field, let G be a finite group. We describe linear G -gradings of the polynomial algebra k[x 1, ..., x m] such that the unit component is a polynomial k-algebra.

Local monomialization of transcendental extensions

Steven Dale CUTKOSKY (2005)

Annales de l’institut Fourier

Suppose that R S are regular local rings which are essentially of finite type over a field k of characteristic zero. If V is a valuation ring of the quotient field K of S which dominates S , then we show that there are sequences of monoidal transforms (blow ups of regular primes) R R 1 and S S 1 along V such that R 1 S 1 is a monomial mapping. It follows that a morphism of nonsingular varieties can be made to be a monomial mapping along a valuation, after blow ups of nonsingular subvarieties.

Loewy coincident algebra and Q F -3 associated graded algebra

Hiroyuki Tachikawa (2009)

Czechoslovak Mathematical Journal

We prove that an associated graded algebra R G of a finite dimensional algebra R is Q F (= selfinjective) if and only if R is Q F and Loewy coincident. Here R is said to be Loewy coincident if, for every primitive idempotent e , the upper Loewy series and the lower Loewy series of R e and e R coincide. Q F -3 algebras are an important generalization of Q F algebras; note that Auslander algebras form a special class of these algebras. We prove that for a Loewy coincident algebra R , the associated graded algebra...

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