Affine semigroup rings

that are complete intersections

Authors:
Klaus G. Fischer, Walter Morris and Jay Shapiro

Journal:
Proc. Amer. Math. Soc. **125** (1997), 3137-3145

MSC (1991):
Primary 13C40; Secondary 14M10

DOI:
https://doi.org/10.1090/S0002-9939-97-03920-8

MathSciNet review:
1401741

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Abstract | References | Similar Articles | Additional Information

Abstract: This paper presents a result concerning the structure of affine semigroup rings that are complete intersections. It generalizes to arbitrary dimensions earlier results for semigroups of dimension less than four. The proof depends on a decomposition theorem for mixed dominating matrices.

**[BCS]**R. A. Brualdi, K. L. Chavey, B. L. Shader,*Rectangular L-matrices*, Linear algebra and its applications, 196 (1994), 37 - 61. MR**95b:15011****[BR]**R. A. Brualdi, H. J. Ryser,*Combinatorial Matrix Theory*, Cambridge University Press, Cambridge (1991). MR**93a:05087****[D]**C. Delorme,*Sous-monoides d'intersection complete de*, Ann. Scient. Ec. Norm Sup., 9 (1976), 145 - 154. MR**53:10821****[FS1]**K. Fischer, J. Shapiro,*Generating prime ideals in the Minkowski ring of polytopes*, Computational Algebra, Marcel Dekker, 151 (1994), 111-130. MR**94m:52014****[FS2]**K. Fischer, J. Shapiro,*Mixed matrices and binomial ideals*, Journal of Pure and Applied Algebra, 113 (1996), 39-54.**[GP]**R. L. Graham, H. O. Pollak,*On addressing problems for loop switching*, Bell System Tech. J. 50 (1971) 2495 - 2519. MR**44:6405****[H]**J. Herzog,*Generators and relations of abelian semigroups and semigroup rings*, Manuscripta Mathematica, 3(1970), 175 - 193. MR**42:4657****[K]**V. Klee,*Recursive structure of S-matrices and an algorithm for recognizing strong sign solvability*, Linear Alg. Appls., 96 (1987), 233 - 247. MR**88j:15002****[RG-S]**J. C. Rosales, Pedro A. García-Sánchez,*On complete intersection affine semigroups*, Communications in Algebra, 23(14) (1995), 5395-5412. MR**96m:14068****[S]**A. Schrijver,*Theory of Linear and Integer Programming*, Wiley, Chichester 1986. MR**88m:90090**

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Additional Information

**Klaus G. Fischer**

Affiliation:
Department of Mathematical Sciences, George Mason University, Fairfax, Virginia 22030

Email:
kfischer@gmu.edu

**Walter Morris**

Affiliation:
Department of Mathematical Sciences, George Mason University, Fairfax, Virginia 22030

Email:
wmorris@gmu.edu

**Jay Shapiro**

Affiliation:
Department of Mathematical Sciences, George Mason University, Fairfax, Virginia 22030

Email:
jshapiro@gmu.edu

DOI:
https://doi.org/10.1090/S0002-9939-97-03920-8

Received by editor(s):
January 22, 1996

Received by editor(s) in revised form:
May 13, 1996

Communicated by:
Wolmer V. Vasconcelos

Article copyright:
© Copyright 1997
American Mathematical Society