zbMATH — the first resource for mathematics

Examples
Geometry Search for the term Geometry in any field. Queries are case-independent.
Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact.
"Topological group" Phrases (multi-words) should be set in "straight quotation marks".
au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted.
Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff.
"Quasi* map*" py: 1989 The resulting documents have publication year 1989.
so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14.
"Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic.
dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles.
py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses).
la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

Operators
a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
Fields
any anywhere an internal document identifier
au author, editor ai internal author identifier
ti title la language
so source ab review, abstract
py publication year rv reviewer
cc MSC code ut uncontrolled term
dt document type (j: journal article; b: book; a: book article)
Indispensable binomials in semigroup ideals. (English) Zbl 1204.13014
The present paper deals with the problem of the uniqueness of a minimal set of binomial generators of a semigroup ideal. The main contribution of the paper is to give necessary and/or sufficient conditions for the uniqueness of such a minimal system of generators. The authors achieve these results by means of the study and combinatorial description of the so-called indispensable binomials in the semigroup ideal. In the first part of the paper, the authors study a combinatorial description of indispensability, giving a combinatorial necessary and sufficient condition for the existence of indispensable binomials in a semigroup ideal (Theorem 8). In this part they also provide an explicit characterization of all indispensable binomials and monomials of a semigroup ideal (Corollary 11). In the second part of the paper, the problem of the existence of indispensable binomials in a semigroup ideal is studied using Gröbner bases. Using these techniques the authors give in Theorem 13 effective necessary conditions for the existence of indispensable binomials. The paper finishes with an example of application of the main results to a problem in Algebraic Statistics.

MSC:
13F20Polynomial rings and ideals
16W50Graded associative rings and modules
13F55Stanley-Reisner face rings; simplicial complexes
WorldCat.org
Full Text: DOI arXiv