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Über den arithmetischen Rang quadratfreier Potenzproduktideale
Author(s) -
Gräbe HansGert
Publication year - 1985
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.19851200118
Subject(s) - mathematics , hilbert's syzygy theorem , monomial , square free integer , arithmetic function , ideal (ethics) , combinatorics , degree (music) , upper and lower bounds , rank (graph theory) , monomial ideal , discrete mathematics , pure mathematics , polynomial ring , mathematical analysis , philosophy , physics , epistemology , acoustics , polynomial
In this paper we give an algorithm to compute an upper bound for the arithmetical rank of squarefree monomial ideals, i.e. the minimal number of hypersurfaces which cut out set‐theoretically the variety of such an ideal. An apriori bound N – a=b +2 is obtained, where N means the number of variables, a the lowest degree in the ideal and b the lowest degree of syzygies in the first syzygy module (Thm. 2). These results sharpen more general results of [2] for the considered class of ideals by methods different from [1], [7].