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

• 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;

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; $\small{{\alpha}}$ $\small{{\in}}$ L[X] a monic irreducible polynomial; $\small{{\xi}}$ any root of in F; and Q = >, the upper to P with respect to $\small{{\alpha}}$. Then R[X]/Q is R-algebra isomorphic to $\small{D[{\xi}]}$; and is R-isomorphic to an overring of D if and only if deg($\small{{\alpha}}$) = 1.
Keywords
Commutative ring;prime ideal;polynomial ring;upper;integral domain;factor ring;degree;
Language
English
Cited by
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