Two Generalizations of the Core Inverse in Rings with Some Applications

Abstract

In this paper, we introduce two new generalized core inverses, namely, the (p,q,m)-core inverse and the ⟨p,q,n⟩-core inverse; both extend the inverses of the ⟨i,m⟩-core inverse, the (j,m)-core inverse, the core inverse, the core-EP inverse and the DMP-inverse.

Keywords

• (<i>p</i>,<i>q</i>,<i>m</i>)-core inverse
• 〈<i>p</i>,<i>q</i>,<i>n</i>〉-core inverse
• 〈i,m〉-core inverse
• (j,m)-core inverse
• core inverse
• DMP-inverse