Arithmetic function

Monomial

Philosophy

Pure mathematics

Discrete mathematics

Rank (graph theory)

Hilbert's syzygy theorem

Degree (music)

Square-free integer

Acoustics

Polynomial

Polynomial ring

Physics

Upper and lower bounds

Ideal (ethics)

Mathematics

Epistemology

Mathematical analysis

Combinatorics

Monomial ideal

Mathematische Nachrichten

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].

Über den arithmetischen Rang quadratfreier Potenzproduktideale