[KSCI] Korea Science Citation Index Service

NOETHERIAN RINGS OF KRULL DIMENSION 2

Shin, Yong-Su (Department of Mathematics, Sungshin Women's University)

Publication Information

Journal of applied mathematics & informatics / v.28, no.3_4, 2010 , pp. 1017-1023 More about this Journal

Abstract

We prove that a maximal ideal M of D[x] has two generators and is of the form where p is an irreducible element in a PID D having infinitely many nonassociate irreducible elements and q(x) is an irreducible non-constant polynomial in D[x]. Moreover, we find how minimal generators of maximal ideals of a polynomial ring D[x] over a DVR D consist of and how many generators those maximal ideals have.

Keywords

Principal ideal domains; polynomial rings; power series rings; discrete valuation rings;

Citations & Related Records

Reference

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