منابع مشابه
The Poincaré Series of Modules over Generic Artinian Gorenstein Algebras of Even Socle Degree
Let Q = k[[x1, . . . , xn]] be the power series ring over a field k. Artinian Gorenstein quotients R = Q/I whose unique maximal ideal m satisfies ms 6= 0 = ms+1 are in correspondence via the Macaulay inverse system with degree s polynomials in n variables. Bøgvad constructed examples for which the Poincaré series of k over R is irrational. When s is even, we prove that such examples are rare. M...
متن کاملGlobal Dimensions of Some Artinian Algebras
The structure of arbitrary associative commutative unital artinian algebras is well-known: they are finite products of associative commutative unital local algebras [6, pg.351, Cor. 23.12]. In the semi-simple case, we have the Artin-Wedderburn Theorem which states that any semi-simple artinian algebra (which is assumed to be associative and unital but not necessarily commutative) is a direct pr...
متن کاملApproach to Artinian Algebras via Natural Quivers
Given an Artinian algebra A over a field k, there are several combinatorial objects associated to A. They are the diagram DA as defined by Drozd and Kirichenko, the natural quiver ΔA defined by Li (cf. Section 2), and a generalized version of k-species (A/r, r/r2) with r being the Jacobson radical of A. When A is splitting over the field k, the diagram DA and the well-known Ext-quiver ΓA are th...
متن کاملNon-level O-sequences of Codimension 3 and Degree of the Socle Elements
It is unknown if an Artinian level O-sequence of codimension 3 and type r (≥ 2) is unimodal, while it is known that any Gorenstein O-sequence of codimension 3 is unimodal. We show that some Artinian non-unimodal O-sequence of codimension 3 cannot be level. We also find another non-level case: if some Artinian algebra A of codimension 3 has the Hilbert function H : h0 h1 · · · hd−1 hd · · · hd }...
متن کاملThe Geometry of the Weak Lefschetz Property and Level Sets of Points
In a recent paper, F. Zanello showed that level Artinian algebras in 3 variables can fail to have the Weak Lefschetz Property (WLP), and can even fail to have unimodal Hilbert function. We show that the same is true for the Artinian reduction of reduced, level sets of points in projective 3-space. Our main goal is to begin an understanding of how the geometry of a set of points can prevent its ...
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ژورنال
عنوان ژورنال: Journal of Algebra
سال: 2018
ISSN: 0021-8693
DOI: 10.1016/j.jalgebra.2018.03.043