Hilbert depth of graded modules over polynomial rings in two variables
| Autor(en): | Moyano-Fernandez, Julio Jose Uliczka, Jan |
Stichwörter: | Commutative graded ring; Finitely generated module; Hilbert depth; Hilbert series; Mathematics; Numerical semigroup | Erscheinungsdatum: | 2013 | Herausgeber: | ACADEMIC PRESS INC ELSEVIER SCIENCE | Enthalten in: | JOURNAL OF ALGEBRA | Band: | 373 | Startseite: | 130 | Seitenende: | 152 | Zusammenfassung: | 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. (C) 2012 Elsevier Inc. All rights reserved. |
ISSN: | 00218693 | DOI: | 10.1016/j.jalgebra.2012.09.026 |
Show full item record
