- Current Issue - Ahead of Print Articles - All Issues - Search - Open Access - Information for Authors - Downloads - Guideline - Regulations ㆍPaper Submission ㆍPaper Reviewing ㆍPublication and Distribution - Code of Ethics - For Authors ㆍOnlilne Submission ㆍMy Manuscript - For Reviewers - For Editors
 An Anderson's theorem on noncommutative rings Bull. Korean Math. Soc. 2008 Vol. 45, No. 4, 797-800 Printed December 1, 2008 Chan Huh, Nam Kyun Kim, and Yang Lee Busan National University, Hanbat National University, and Busan National University Abstract : Let $R$ be a ring and $I$ be a proper ideal of $R$. For the case of $R$ being commutative, Anderson proved that $(*)$ there are only finitely many prime ideals minimal over $I$ whenever every prime ideal minimal over $I$ is finitely generated. We in this note extend the class of rings that satisfies the condition $(*)$ to noncommutative rings, so called homomorphically IFP, which is a generalization of commutative rings. As a corollary we obtain that there are only finitely many minimal prime ideals in the polynomial ring over $R$ when every minimal prime ideal of a homomorphically IFP ring $R$ is finitely generated. Keywords : commutative ring, (homomorphically) IFP ring, minimal prime ideal MSC numbers : 16D25, 16N60 Downloads: Full-text PDF