Journal article
Ikeda–Nakayama Rings
Journal of algebra, Vol.226(2), pp.1001-1010
04/15/2000
DOI: 10.1006/jabr.1999.8217
Abstract
A ring R is called a right Ikeda-Nakayama ring (right IN-ring) if the left annihilator of the intersection of any two right ideals is the sum of the two left annihilators. In this paper we show that if R is a right IN-ring and A and B are right ideals of R that are complements of each other, there exists an idempotent e in R such that A=eR and B=(1−e)R. As a consequence we show that R is right selfinjective if and only if M2(R) is a right IN-ring. It is also shown that R is a dual ring if and only if R is a left and right IN-ring and the dual of every simple right R-module is simple. Finally, we prove that R is quasi-Frobenius if and only if R is a left perfect, left and right IN-ring, extending work on both selfinjective rings and dual rings. Several examples are provided to show that our results are non-trivial extensions of the known results on the subject.
Details
- Title: Subtitle
- Ikeda–Nakayama Rings
- Creators
- V Camillo - University of IowaW.K Nicholson - University of CalgaryM.F Yousif - The Ohio State University
- Resource Type
- Journal article
- Publication Details
- Journal of algebra, Vol.226(2), pp.1001-1010
- DOI
- 10.1006/jabr.1999.8217
- ISSN
- 0021-8693
- eISSN
- 1090-266X
- Publisher
- Elsevier Inc
- Language
- English
- Date published
- 04/15/2000
- Academic Unit
- Mathematics
- Record Identifier
- 9984240768702771
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