Advanced SearchSearch Tips
The Factor Domains that Result from Uppers to Prime Ideals in Polynomial Rings
facebook(new window)  Pirnt(new window) E-mail(new window) Excel Download
  • Journal title : Kyungpook mathematical journal
  • Volume 50, Issue 1,  2010, pp.1-5
  • Publisher : Department of Mathematics, Kyungpook National University
  • DOI : 10.5666/KMJ.2010.50.1.001
 Title & Authors
The Factor Domains that Result from Uppers to Prime Ideals in Polynomial Rings
Dobbs, David Earl;
  PDF(new window)
Let P be a prime ideal of a commutative unital ring R; X an indeterminate; D := R/P; L the quotient field of D; F an algebraic closure of L; L[X] a monic irreducible polynomial; any root of in F; and Q = >, the upper to P with respect to . Then R[X]/Q is R-algebra isomorphic to ; and is R-isomorphic to an overring of D if and only if deg() = 1.
Commutative ring;prime ideal;polynomial ring;upper;integral domain;factor ring;degree;
 Cited by
T. Albu, On a paper of Uchida concerning simple finite extensions of Dedekind domains, Osaka J. Math., 16(1979), 65-69.

A. Bouvier, D. E. Dobbs and M. Fontana, Universally catenarian integral domains, Adv. Math., 72(1988), 211-238. crossref(new window)

D. E. Dobbs and M. Fontana, Universally incomparable ring-homomorphisms, Bull. Austral. Math. Soc., 29(1984), 289-302. crossref(new window)

D. E. Dobbs and J. Shapiro, A classification of the minimal ring extensions of an integral domain, J. Algebra, 305(2006), 185-193. crossref(new window)

I. Kaplansky, Commutative Rings, rev. ed., Univ. Chicago Press, Chicago, 1974.

S. McAdam, Going down in polynomial rings, Can. J. Math., 23(1971), 704-711. crossref(new window)

K. Uchida, When is Z[$\alpha$] the ring of integers?, Osaka J. Math., 14(1977), 155-157.

H. Uda, Incomparability in ring extensions, Hiroshima Math. J., 9(1979), 451-463.