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

Discussiones Mathematicae - General Algebra and Applications (2003)

- Volume: 23, Issue: 1, page 5-11
- ISSN: 1509-9415

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topLuis F. Cáceres-Duque. "An effective procedure for minimal bases of ideals in Z[x]." Discussiones Mathematicae - General Algebra and Applications 23.1 (2003): 5-11. <http://eudml.org/doc/287707>.

@article{LuisF2003,

abstract = {We give an effective procedure to find minimal bases for ideals of the ring of polynomials over the integers.},

author = {Luis F. Cáceres-Duque},

journal = {Discussiones Mathematicae - General Algebra and Applications},

keywords = {ideals; minimal bases for ideals; polynomials over integers},

language = {eng},

number = {1},

pages = {5-11},

title = {An effective procedure for minimal bases of ideals in Z[x]},

url = {http://eudml.org/doc/287707},

volume = {23},

year = {2003},

}

TY - JOUR

AU - Luis F. Cáceres-Duque

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

JO - Discussiones Mathematicae - General Algebra and Applications

PY - 2003

VL - 23

IS - 1

SP - 5

EP - 11

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

LA - eng

KW - ideals; minimal bases for ideals; polynomials over integers

UR - http://eudml.org/doc/287707

ER -

## References

top- [1] C.W. Ayoub, On Constructing Bases for Ideals in Polynomial Rings over the Integers, J. Number Theory 17 (1983), 204-225. Zbl0516.13018
- [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 Z[x] and Zpn[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. Zbl0265.13011
- [6] H. Simmons, The Solution of a Decision Problem for Several Classes of Rings, Pacific J. Math. 34 (1970), 547-557. Zbl0198.02701
- [7] G. Szekeres, A canonical basis for the ideals of a polynomial domain, Amer. Math. Monthly 59 (1952), 379-386. Zbl0047.03303

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