Skip to content

Go to Sitemap

Download PDF - An effective procedure for minimal bases of ideals in Z[x] All rights reserved. Copyright exceptions and limitations apply

ArticleOriginal scientific text

Title

An effective procedure for minimal bases of ideals in Z[x]

Authors ¹

Affiliations

Mathematics Department, University of Puerto Rico at Mayagüez, PO BOX 9018 Mayagüez, PR 00681, USA

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

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