[KSCI] Korea Science Citation Index Service

http://dx.doi.org/10.5666/KMJ.2010.50.1.001

The Factor Domains that Result from Uppers to Prime Ideals in Polynomial Rings

Dobbs, David Earl (Department of Mathematics, University of Tennessee)

Publication Information

Kyungpook Mathematical Journal / v.50, no.1, 2010 , pp. 1-5 More about this Journal

Abstract

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; ${\alpha}$ ${\in}$ L[X] a monic irreducible polynomial; ${\xi}$ any root of in F; and Q = >, the upper to P with respect to ${\alpha}$ . Then R[X]/Q is R-algebra isomorphic to $D[{\xi}]$ ; and is R-isomorphic to an overring of D if and only if deg( ${\alpha}$ ) = 1.

Keywords

Commutative ring; prime ideal; polynomial ring; upper; integral domain; factor ring; degree;

Citations & Related Records

Times Cited By SCOPUS : 0

Reference

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