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;
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.