Artinian Level Algebras of Low Socle Degree
نویسندگان
چکیده
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...
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We find a sufficient condition that H is not level based on a reduction number. In particular, we prove that a graded Artinian algebra of codimension 3 with Hilbert function H = (h0, h1, . . . , hd−1 > hd = hd+1) cannot be level if hd ≤ 2d + 3, and that there exists a level Osequence of codimension 3 of type H for hd ≥ 2d+k for k ≥ 4. Furthermore, we show that H is not level if β1,d+2(I ) = β2,...
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ژورنال
عنوان ژورنال: Communications in Algebra
سال: 2013
ISSN: 0092-7872,1532-4125
DOI: 10.1080/00927872.2012.722736