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How to compute the multigraded Hilbert depth of a module
Author(s) -
Ichim Bogdan,
MoyanoFernández JulioJosé
Publication year - 2014
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.201300120
Subject(s) - mathematics , computation , hilbert–poincaré series , hilbert's fourteenth problem , set (abstract data type) , finitely generated abelian group , polynomial ring , polynomial , hilbert's basis theorem , hilbert r tree , pure mathematics , ring (chemistry) , algebra over a field , hilbert series and hilbert polynomial , hilbert space , rigged hilbert space , algorithm , mathematical analysis , computer science , reproducing kernel hilbert space , programming language , chemistry , organic chemistry
In the first part of this paper we introduce a method for computing Hilbert decompositions (and consequently the Hilbert depth) of a finitely generated multigraded module M over the polynomial ring K [ X 1 , ... , X n ] by reducing the problem to the computation of the finite set of the new defined Hilbert partitions. In the second part we show how Hilbert partitions may be used for computing the Stanley depth of the module M . In particular, we answer two open questions posed by Herzog in [8][J. Herzog, 2013].