Monomial Gorenstein ideals
Copyright policy )Monomial Gorenstein ideals
The paper concerns itself with generating sets for monomial Gorenstein ideals in polynomial rings k[x1,..., xr], k an arbitrary field. For r=5 it is shown that for a certain class of these ideals, the number of generators is bounded by 13. To establish the sharpness of this bound an algorithm is established, to obtain all numerical symmetric semigroups with a fixed odd integer 2n+1 as last integer unattained. Finally, a short proof of the known fact is given, that for r=4 the number of elements in a generating set is 3 or 5.
- University of Maine United States
polynomial ring, Special algebraic curves and curves of low genus, Free semigroups, generators and relations, word problems, Special types (Cohen-Macaulay, Gorenstein, Buchsbaum, etc.), Singularities in algebraic geometry, generating sets for monomial Gorenstein ideals, Commutative rings defined by factorization properties (e.g., atomic, factorial, half-factorial), Polynomial rings and ideals; rings of integer-valued polynomials, Commutative rings and modules of finite generation or presentation; number of generators, minimal number of generators, Varieties defined by ring conditions (factorial, Cohen-Macaulay, seminormal), monomial Gorenstein ideal, monomial curve, semigroups of integers
polynomial ring, Special algebraic curves and curves of low genus, Free semigroups, generators and relations, word problems, Special types (Cohen-Macaulay, Gorenstein, Buchsbaum, etc.), Singularities in algebraic geometry, generating sets for monomial Gorenstein ideals, Commutative rings defined by factorization properties (e.g., atomic, factorial, half-factorial), Polynomial rings and ideals; rings of integer-valued polynomials, Commutative rings and modules of finite generation or presentation; number of generators, minimal number of generators, Varieties defined by ring conditions (factorial, Cohen-Macaulay, seminormal), monomial Gorenstein ideal, monomial curve, semigroups of integers
selected citations These citations are derived from selected sources.This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).9 popularity This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.Average influence This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).Top 10% impulse This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.Average
Citations provided by BIP!Popularity provided by BIP!