An effective procedure for minimal bases of ideals in Z[x]
Luis F. Cáceres-Duque
Discussiones Mathematicae - General Algebra and Applications, Tome 23 (2003), p. 5-11 / Harvested from The Polish Digital Mathematics Library

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

Publié le : 2003-01-01
EUDML-ID : urn:eudml:doc:287707
@article{bwmeta1.element.bwnjournal-article-doi-10_7151_dmgaa_1059,
     author = {Luis F. C\'aceres-Duque},
     title = {An effective procedure for minimal bases of ideals in Z[x]},
     journal = {Discussiones Mathematicae - General Algebra and Applications},
     volume = {23},
     year = {2003},
     pages = {5-11},
     zbl = {1108.13302},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmgaa_1059}
}
Luis F. Cáceres-Duque. An effective procedure for minimal bases of ideals in Z[x]. Discussiones Mathematicae - General Algebra and Applications, Tome 23 (2003) pp. 5-11. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmgaa_1059/

[000] [1] C.W. Ayoub, On Constructing Bases for Ideals in Polynomial Rings over the Integers, J. Number Theory 17 (1983), 204-225. | Zbl 0516.13018

[001] [2] L.F. Cáceres-Duque, Ultraproduct of Sets and Ideal Theories of Commutative Rings, Ph.D. dissertation, University of Iowa, Iowa City, IA, 1998.

[002] [3] C.B. Hurd, Concerning Ideals in Z[x] and Zpn[x], Ph.D. dissertation, Pennsylvania State University, University Park, PA, 1970.

[003] [4] L. Redei, Algebra, Vol 1, Pergamon Press, London 1967.

[004] [5] F. Richman, Constructive Aspects of Noetherian Rings, Proc. Amer. Math. Soc. 44 (1974), 436-441. | Zbl 0265.13011

[005] [6] H. Simmons, The Solution of a Decision Problem for Several Classes of Rings, Pacific J. Math. 34 (1970), 547-557. | Zbl 0198.02701

[006] [7] G. Szekeres, A canonical basis for the ideals of a polynomial domain, Amer. Math. Monthly 59 (1952), 379-386. | Zbl 0047.03303