Biography

Dr. Huanyin Chen
Hangzhou Normal University, China
Title: On Hirano inverses in rings
Abstract:
We introduce and study a new class of generalized inverses in rings. An element $a$ in a ring has Hirano inverse $b$ if $a^2-ab\in N(R), ab=ba~\mbox{and}~b=bab.$ This is the dual of Drazin inverses in rings. We prove that an element $a\in R$ has Hirano inverse if and only if $a^2$ has strongly Drazin inverse, if and only if $a-a^3\in N(R)$. If $\frac{1}{2}\in R$, we prove that $a\in R$ has Hirano inverse if and only if there exists $p^3=p\in comm^2(a)$ such that $a-p\in N(R)$, if and only if there exist two idempotents $e,f\in comm^2(a)$ such that $a+e-f\in N(R)$. Clines formula and additive results for this generalized inverse are thereby obtained.
Biography:
Huanyin Chen was born in Jiangsu, China. He got his Ph D. degree from Nanjing University in 1995. His main research interests are noncommutative rings (especially exchange rings, regular rings, clean rings), stable range conditions; topology and $C^*$-algebra. For the past twenty years, he published about 310 articles on algebras. These works covered categories, homological algebras and ring theory. As professional activities, he is the editor of International Electronic Journal of Algebra, The Journal for Algebra and Number Theory Academia, and Journal of Hangzhou Normal University. For further information, please refer to https://www.researchgate.net/profile/Huanyin_Chen