Back to Search
Start Over
A class of uniquely (strongly) clean rings
- Source :
- Volume: 38, Issue: 1 40-51, Turkish Journal of Mathematics
- Publication Year :
- 2014
- Publisher :
- TÜBİTAK, 2014.
-
Abstract
- In this paper we call a ring R delta(r)-clean if every element is the sum of an idempotent and an element in delta(R-R) where delta(R-R) is the intersection of all essential maximal right ideals of R. If this representation is unique (and the elements commute) for every element we call the ring uniquely (strongly) delta(r)-clean. Various basic characterizations and properties of these rings are proved, and many extensions are investigated and many examples are given. In particular, we see that the class of delta(r)-clean rings lies between the class of uniquely clean rings and the class of exchange rings, and the class of uniquely strongly delta(r)-clean rings is a subclass of the class of uniquely strongly clean rings. We prove that R is delta(r)-clean if and only if R/delta(r)(R-R) is Boolean and R/Soc(R-R) is clean where Soc(R-R) is the right socle of R.
Details
- Language :
- Turkish
- ISSN :
- 13000098 and 13036149
- Database :
- OpenAIRE
- Journal :
- Volume: 38, Issue: 1 40-51, Turkish Journal of Mathematics
- Accession number :
- edsair.doi.dedup.....63226a1fea6d47ce104140742778c40e