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The purpose of this note is to introduce a multiplication on the set of homogeneous polynomials of fixed degree d, in a way to provide a duality theory between monomial ideals of K[x_1,ldots,x_d] generated in degrees leq n and block stable ideals (a class of ideals containing the Borel fixed ones) of K[x_1,ldots,x_n] generated in degree d. As a byproduct we give a new proof of the characterization of Betti tables of ideals with linear resolution given by Murai.
In this paper, we make the notion of approximating an Artinian local ring by a Gorenstein Artin local ring precise using the concept of Gorenstein colength. We also answer the question as to when the Gorenstein colength is at most two.
We give a detailed proof for Gordan-Noethers results in Ueber die algebraischen Formen, deren Hessesche Determinante identisch verschwindet published in 1876 in Mathematische Annahlen. C. Lossen has written a paper in a similar direction as the prese
In this paper it is shown that a polyomino is balanced if and only if it is simple. As a consequence one obtains that the coordinate ring of a simple polyomino is a normal Cohen-Macaulay domain.
Let $R=mathbf{C}[xi_1,xi_2,ldots]$ be the infinite variable polynomial ring, equipped with the natural action of the infinite symmetric group $mathfrak{S}$. We classify the $mathfrak{S}$-primes of $R$, determine the containments among these ideals, a
We begin the study of the notion of diameter of an ideal I of a polynomial ring S over a field, an invariant measuring the distance between the minimal primes of I. We provide large classes of Hirsch ideals, i.e. ideals with diameter not larger than