Let R be an associative ring with unity 1. The main contribution of this paper is to introduce the notion of generalized quasipolar elements in R as an extension of quasipolar elements of Koliha and Patrício. Several necessary and sufficient conditions of \(a\in R\) to be generalized quasipolar are derived. Then, we define a class of outer generalized inverses, called weakly generalized Drazin inverses generalizing Koliha’s generalized Drazin inverses. It is shown that \(a\in R\) has a weakly generalized Drazin inverse if and only if it is generalized quasipolar. Finally, existence criteria for weakly generalized Drazin inverses are obtained.

令R为具有1的缔合环。本文的主要贡献是引入R中的广义拟极元素的概念，作为Koliha和Patrício拟极元素的扩展。推导了要泛化为拟极性的\（a \ in R \）的几个充要条件。然后，我们定义一类外部广义逆，称为弱广义Drazin逆，广义Koliha的广义Drazin逆。证明\（a \ in R \）在且仅当是广义拟极时具有弱广义Drazin逆。最后，获得了弱广义Drazin逆的存在准则。