# 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)
Construction of set theoretic complete intersections via semigroup gluing. (English) Zbl 0944.14018
Summary: We present a very simple, but powerful, technique for finding monomial varieties which are set theoretic complete intersections. The technique is based on the concept of gluing semigroups that was defined by {\it J. C. Rosales} [Semigroup Forum 55, No. 2, 152-159 (1997)] and used by {\it K. G. Fischer, W. Morris} and {\it J. Shapiro} [Proc. Am. Math. Soc. 125, No. 11, 3137-3145 (1997; Zbl 0893.20047)] to characterize complete intersection affine semigroup rings. There are several techniques in the literature proving that certain varieties are set theoretic complete intersections but all of them preserve the dimension of the variety and are mainly results about curves. The technique presented here does not preserve necessarily the dimension of the variety and it can combine the known results to produce set theoretic complete intersection varieties of any dimension, see examples 4 and 5.

##### MSC:
 14M10 Complete intersections 20M25 Semigroup rings, multiplicative semigroups of rings
Full Text: