2013/10/11 by Orhan Gürgün, Gürgün, Orhan
Mathematics · #15A09 #16S10 #FOS: Mathematics #Rings and Algebras (math.RA) #math.RA #msc:15A09 #msc:16S10
paper · pdf · doi:10.48550/arxiv.1310.3303
9 pages
arxiv created 2013/10/11 · arxiv updated 2013/10/15
In \citeC, LCC, it is proven that if an element ab in a ring is (generalized) Drazin invertible, then so is ba. In this paper, we give a new and short proof of it in an effective manner. In particular, we show that if ab is strongly clean, then so is ba. Consequently, we see that if 1-ab is strongly clean, then so is 1-ba. Also, some characterizations are obtained for some certain elements in a corner ring. It is shown that for an idempotent e and any arbitrary element a in a ring, ea+1-e is Drazin invertible if and only if eae is Drazin invertible.