On group invertibility in rings

Abstract

We prove some results for the group inverse of elements in a unital ring. Thus, some results from (C. Deng, Electronic J. Linear Algebra 31 (2016)) are extended to more general settings.

Perturbation for group inverse in a Banach algebra

“…Obviously, [9,Theorem 2.1] and the invertibility of a 1 + b 1 , we derive that a + b is group invertible if and only if (a + b)a π is group invertible. In this case,…”

The group inverse of the sum in a Banach algebra

“…The group invertibility in a Banach algebra is attractive. Many authors have studied such problems from many different views, e.g., [1,5,6,7,10]. It was also extensively investigated under the concept "strongly regularity" in ring theory.…”

The Holocene Environmental Evolution of the Inner Hangzhou Bay and Its Significance

“…It has interesting applications of resistance distances to the bipartiteness of graphs (see [5,13]). Recently, the group inverse in a Banach algebra or a ring was extensively studied by many authors, e.g., [1,2,4,6,10,11,14]. In [9, Theorem 2.3], Liu et al presented the group inverse of the combinations of two group invertible complex matrices P and Q under the condition P QQ # = QP P # .…”