منابع مشابه
Polynomial Rings with a Pivotal Monomial1
1. Amitsur in his paper on Finite Dimensional Central Division Algebras [l] has proved that in a division ring D with center C, (P: C) 5= ra2 < =o if and only if every primitive homomorphic image of a polynomial ring P[x] is a complete matrix ring Ah, h^n, over a division ring A. Equivalently speaking, a division ring is finite dimensional over its center if and only if the polynomial ring over...
متن کاملDifferential operators on monomial rings
Rings of differential operators are notoriously difficult to compute. This paper computes the ring of differential operators on a Stanley-Reisner ring R. The D-module structure of R is determined. This yields a new proof that Nakai’s conjecture holds for Stanley-Reisner rings. An application to tight closure is described. @ 1999 Elsevier Science B.V. All rights reserved. AMS Clas.@cation: Prima...
متن کاملPoincaré Series of Monomial Rings
Let k be a field, let I be an ideal generated by monomials in the polynomial ring k[x1, . . . , xt] and let R = k[x1, . . . , xt]/I be the associated monomial ring. The k-vector spaces Tori (k, k) are N -graded. We derive a formula for the multigraded Poincaré series of R, PRk (x, z) = ∑ i≥0,α∈Nt dimk Tor R i,α(k, k)x z, in terms of the homology of certain simplicial complexes associated to sub...
متن کاملRees cones and monomial rings of matroids
Using linear algebra methods we study certain algebraic properties of monomial rings and matroids. Let I be a monomial ideal in a polynomial ring over an arbitrary field. If the Rees cone of I is quasi-ideal, we express the normalization of the Rees algebra of I in terms of an Ehrhart ring. We introduce the basis Rees cone of a matroid (or a polymatroid) and study their facets. Some application...
متن کاملThe Auslander-reiten Translate on Monomial Rings
For t in N, E.Miller has defined a category of positively t-determined modules over the polynomial ring S in n variables. We consider the AuslanderReiten translate, Nt, on the (derived) category of such modules. A monomial ideal I is t-determined if each generator x has a ≤ t. We compute the multigraded cohomology and betti spaces of N k t (S/I) for every iterate k and also the S-module structu...
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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 1958
ISSN: 0002-9939
DOI: 10.2307/2033222