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Discussiones Mathematicae General Algebra and Applications 23(1) (2003) 5-11
DOI: https://doi.org/10.7151/dmgaa.1059

AN EFFECTIVE PROCEDURE FOR MINIMAL
BASES OF IDEALS IN Z[x]

Luis F. Cáceres-Duque

Mathematics Department, University of Puerto Rico at Mayagüez,
PO BOX 9018 Mayagüez, PR 00681, USA
e-mail: lcaceres@math.uprm.edu

Abstract

We give an effective procedure to find minimal bases for ideals of the ring of polynomials over the integers.

Keywords: ideals, minimal bases for ideals, polynomials over integers.

2000 Mathematics Subject Classification: 11C08, 13F20, 11A07, 11Y99.

References

[1]	C.W. Ayoub, On Constructing Bases for Ideals in Polynomial Rings over the Integers, J. Number Theory 17 (1983), 204-225.
[2]	L.F. Cáceres-Duque, Ultraproduct of Sets and Ideal Theories of Commutative Rings, Ph.D. dissertation, University of Iowa, Iowa City, IA, 1998.
[3]	C.B. Hurd, Concerning Ideals in \mathbbZ [x] and \mathbbZpn [x], Ph.D. dissertation, Pennsylvania State University, University Park, PA, 1970.
[4]	L. Redei, Algebra, Vol 1, Pergamon Press, London 1967.
[5]	F. Richman, Constructive Aspects of Noetherian Rings, Proc. Amer. Math. Soc. 44 (1974), 436-441.
[6]	H. Simmons, The Solution of a Decision Problem for Several Classes of Rings, Pacific J. Math. 34 (1970), 547-557.
[7]	G. Szekeres, A canonical basis for the ideals of a polynomial domain, Amer. Math. Monthly 59 (1952), 379-386.

Received 18 April 2002
Revised 12 February 2003