arXiv subjects

Orhan Gürgün

Publications and source records attributed to Orhan Gürgün.

2 recordsLinked to original sources

arXiv2014

Extensions of Quasipolar Rings

In this paper we define and study quasipolar general rings (with or without identity) and extend many of the basic results to the wider class. We obtain some new characterizations of quasipolar and strongly $π$-regular elements by using quasipolar general rings. We see that quasipolar general rings lies between strongly $π$-regular and strongly clean general rings. Consequently, we prove that $R$ is pseudopolar if and only if $R$ is strongly $π$-rad clean and quasipolar.

math.RA↗

arXiv2013

On Cline's Formula for some certain elements in a ring

In \cite{C, 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.

math.RA↗