DM-GAA

ISSN 1509-9415 (print version)

ISSN 2084-0373 (electronic version)

https://doi.org/10.7151/dmgaa

Discussiones Mathematicae - General Algebra and Applications

Cite Score: 0.4

SJR: 0.203

SNIP: 0.562

MCQ: 0.12

Index Copernicus: 121.02

Discussiones Mathematicae - General Algebra and Applications

PDF

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


Close