%0 Journal Article
%T Additive Property of Drazin Invertibility of Elements
%A Long Wang
%A Huihui Zhu
%A Xia Zhu
%A Jianlong Chen
%J Mathematics
%D 2013
%I arXiv
%X In this article, we investigate additive properties of the Drazin inverse of elements in rings and algebras over an arbitrary field. Under the weakly commutative condition of $ab = \lambda ba$, we show that $a-b$ is Drazin invertible if and only if $aa^{D}(a-b)bb^{D}$ is Drazin invertible. Next, we give explicit representations of $(a+b)^{D}$, as a function of $a, b, a^{D}$ and $b^{D}$, under the conditions $a^{3}b = ba$ and $b^{3}a = ab$.
%U http://arxiv.org/abs/1307.3816v1