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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826 (e) ISSN 0002-9939 (p)
     

Affine semigroup rings that are complete intersections

Author(s): Klaus G. Fischer; Walter Morris; Jay Shapiro
Journal: Proc. Amer. Math. Soc. 125 (1997), 3137-3145.
MSC (1991): Primary 13C40; Secondary 14M10
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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.


References:

[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 $\mathbf {N}$, 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 $O(m^2)$ 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: 10.1090/S0002-9939-97-03920-8
PII: S 0002-9939(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
Copyright of article: Copyright 1997, American Mathematical Society


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