Journal article
QUASI-MORPHIC RINGS
Journal of algebra and its applications, Vol.6(5), pp.789-799
10/2007
DOI: 10.1142/S0219498807002454
Abstract
A ring R is called left morphic if R/Ra ≅ l(a) for each a ∈ R, equivalently if there exists b ∈ R such that Ra = l(b) and l(a) = Rb. In this paper, we ask only that b and c exist such that Ra = l(b) and l(a) = Rc, and call R left quasi-morphic if this happens for every element a of R. This class of rings contains the regular rings and the left morphic rings, and it is shown that finite intersections of principal left ideals in such a ring are again principal. It is further proved that if R is quasi-morphic (left and right), then R is a Bézout ring and has the ACC on principal left ideals if and only if it is an artinian principal ideal ring.
Details
- Title: Subtitle
- QUASI-MORPHIC RINGS
- Creators
- V Camillo - University of IowaW. K Nicholson - University of Calgary
- Resource Type
- Journal article
- Publication Details
- Journal of algebra and its applications, Vol.6(5), pp.789-799
- Publisher
- World Scientific Publishing Company
- DOI
- 10.1142/S0219498807002454
- ISSN
- 0219-4988
- eISSN
- 1793-6829
- Language
- English
- Date published
- 10/2007
- Academic Unit
- Mathematics
- Record Identifier
- 9984242453102771
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