Characterization of multiplication commutative rings with finitely many minimal prime ideals. Issue 11 (2nd November 2019)

• Record Type: Journal Article
• Authors: Alsuraiheed, T.; Bavula, V. V.
• Is Part Of: Communications in algebra. Volume 47:Issue 11(2019)
• Page Start: 4533
• Page End: 4540
• Publication Date: 2019-11-02
• Subjects: Artinian local principal ideal ring -- Dedekind domain -- multiplication ideal -- multiplication module -- multiplication ring; 13C05 -- 13E05 -- 13F05 -- 13F10; Algebra -- Periodicals; 512.005
• DOI: 10.1080/00927872.2018.1543428
• Languages: English
• ISSNs: 0092-7872

Abstract

Abstract: 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 ∏ i = 1 n D i where Di 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.).