中文摘要：

为一个复杂矩阵的核心逆被 O. M 介绍。Baksalary 和 G。Trenkler。D. S。葡萄酒， N。 .Dini 和 D. S。Djordjevi 在一枚戒指概括了一个复杂矩阵的核心逆到一个元素的格。他们也证明在一枚戒指的一个元素的核心逆能被五个方程和每个核心描绘可颠倒的元素组可颠倒。问什么时候是自然的一个组可颠倒的元素核心可颠倒。在这份报纸，我们将回答这个问题。让 R 是有复杂物的一枚戒指，我们将使用三个方程描绘一个元素的核心逆。也就是说让一， b R。那么有 a#= b 的 R# 如果并且仅当(ab )*= ab， ba ²= 一，并且 ab ²= b。最后，我们调查二个核心的添加剂性质可颠倒的元素。而且，二个核心的和的公式可颠倒的元素被介绍。

英文摘要：

The core inverse for a complex matrix was introduced by O. M. Baksalary and G. Trenkler. D. S. Rakic, N. C. Dincic and D. S. Djordjevc generalized the core inverse of a complex matrix to the case of an element in a ring. They also proved that the core inverse of an element in a ring can be characterized by five equations and every core invertible element is group invertible. It is natural to ask when a group invertible element is core invertible. In this paper, we will answer this question. Let R be a ring with involution, we will use three equations to characterize the core inverse of an element. That is, let a,b ∈ R. Then a ∈ R with a= b if and only if （ab）^＊ = ab, ba^2 = a, and ab^2 = b. Finally, we investigate the additive property of two core invertible elements. Moreover, the formulae of the sum of two core invertible elements are presented.