Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
6414901 | Journal of Algebra | 2013 | 23 Pages |
Abstract
In this article we mainly consider the positively Z-graded polynomial ring R=F[X,Y] over an arbitrary field F and Hilbert series of finitely generated graded R-modules. The central result is an arithmetic criterion for such a series to be the Hilbert series of some R-module of positive depth. In the generic case, that is deg(X) and deg(Y) being coprime, this criterion can be formulated in terms of the numerical semigroup generated by those degrees.
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
Julio José Moyano-Fernández, Jan Uliczka,