Characterization of multiplication commutative rings with finitely many minimal prime ideals

被引:7
作者
Alsuraiheed, T. [1 ]
Bavula, V. V. [1 ]
机构
[1] Univ Sheffield, Sch Math & Stat, Hicks Bldg, Sheffield S3 7RH, S Yorkshire, England
关键词
Artinian local principal ideal ring; Dedekind domain; multiplication ideal; multiplication module; multiplication ring;
D O I
10.1080/00927872.2018.1543428
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
The aim of the article is to give a characterization of a multiplication commutative ring with finitely many minimal prime ideals: Each such ring is a finite direct product of rings where D-i is either a Dedekind domain or an Artinian, local, principal ideal ring and vice versa. In particular, each such ring is a Noetherian ring. As a corollary subclasses of such rings are described (semiprime, Artinian, semiprime and Artinian, local, domain, etc.).
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页码:4533 / 4540
页数:8
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