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

• Autorzy: Luis F. Cáceres-Duque
• Języki publikacji: EN

Abstrakty

EN

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

Słowa kluczowe

EN

ideals; minimal bases for ideals; polynomials over integers

Kategorie tematyczne

• 11Y99: None of the above, but in this section
• 11C08: Polynomials
• 13F20: Polynomial rings and ideals; rings of integer-valued polynomials
• 11A07: Congruences; primitive roots; residue systems

• Wydawca: Faculty of Mathematics, Computer Science and Econometrics, University of Zielona Góra
• Czasopismo: Discussiones Mathematicae - General Algebra and Applications
• Rocznik: 2003
• Tom: 23
• Numer: 1
• Strony: 5-11

Daty

wydano

2003

otrzymano

2002-04-18

poprawiono

2003-02-12

Twórcy

autor

Luis F. Cáceres-Duque

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

Bibliografia

• [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 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.
• [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.

Identyfikatory

DOI

10.7151/dmgaa.1059