Please use this identifier to cite or link to this item:
Title: On locally divided rings and going-down rings
Authors: Badawi, Ayman 
Dobbs, David E. 
Keywords: Commutative rings
Issue Date: 2001
Publisher: Communications in Algebra
Abstract: All rings considered below are commutative with 1. As in [B2], if R is a ring, P 2 SpecðRÞ is a divided prime ideal in R if P is comparable under inclusion to each ideal of R; and R is a divided ring if each P 2 SpecðRÞ is divided in R. Divided rings generalize the divided domains introduced in [D2]. Our main goal is to generalize another class of domains introduced in [D2], the locally divided domains. We say that a ring R is a locally divided ring if RP is a divided ring for each P 2 SpecðRÞ. Each divided ring is locally divided [B2, Proposition 4]. Since the literature on locally divided domains ([D2], [D4], [DF]) is tied to studies of going-down domains (in the sense of [D1]), it is natural to pursue connections between locally divided rings and the recently introduced going-down rings [D5]. Section 3 develops several such connections, some with the flavor of domain-theoretic studies and others differing from such phenomena in the presence of zero-divisors. First, Section 2 develops more information about divided rings and initiates the theory of locally divided rings.
DOI: 10.1081/AGB-4988
Appears in Collections:Fulltext Publications

Files in This Item:
File Description SizeFormat
On locally divided rings and going-down rings.pdf388.6 kBAdobe PDFView/Open
Show full item record

Page view(s)

checked on Jun 27, 2024


checked on Jun 27, 2024

Google ScholarTM



Items in DSpace are protected by copyright, with all rights reserved, unless otherwise indicated.