Kaplansky-type Theorems, II

• Journal title : Kyungpook mathematical journal
• Volume 51, Issue 3,  2011, pp.339-344
• Publisher : Department of Mathematics, Kyungpook National University
• DOI : 10.5666/KMJ.2011.51.3.339
Title & Authors
Kaplansky-type Theorems, II
Chang, Gyu-Whan; Kim, Hwan-Koo;

Abstract
Let D be an integral domain with quotient field K, X be an indeterminate over D, and D[X] be the polynomial ring over D. A prime ideal Q of D[X] is called an upper to zero in D[X] if Q = fK[X] $\small{{\cap}}$ D[X] for some f $\small{{\in}}$ D[X]. In this paper, we study integral domains D such that every upper to zero in D[X] contains a prime element (resp., a primary element, a t-invertible primary ideal, an invertible primary ideal).
Keywords
Kaplansky theorem;upper to zero in D[X];prime (primary) element;
Language
English
Cited by
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Kyungpook mathematical journal, 2011. vol.51. 3, pp.339-344
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