We present some new characterizations for the pseudo core inverse in rings with involution. Firstly, we characterize the pseudo core inverse by a unique projection. Secondly, we prove that the pseudo core inverse is EP and obtain another expression of the pseudo core inverse. Furthermore, we establish the relation between the EP element and the pseudo core inverse. Finally, maximal classes of elements in rings determining the pseudo core inverse are investigated.

中文翻译：

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与伪核逆相关的元素的特征和最大类别

我们提出了具有对合环的伪核逆的一些新特征。首先，我们通过唯一的投影来表征伪核逆。其次，证明伪核逆为EP，得到伪核逆的另一种表达式。此外，我们建立了 EP 元素和伪核逆之间的关系。最后，研究了确定伪核逆的环中元素的最大类别。