伪核逆的广义Cline公式和广义Jacobson引理

Generalized Cline's Formula and Generalized Jacobson's Lemma for Pseudo Core Inverse

在*-环中,我们研究了伪核逆的广义Cline公式和广义Jacobson引理。讨论了在dbd=acd,bdb=bac条件或dbd=acd,aca=dba条件下,当1-ac(或ac)有伪核逆时,1-bd(或bd)有伪核逆的等价条件。进一步地,通过1-ac(或ac)的伪核逆给出了1-bd(或bd)的伪核逆的表达式。

In a ring with involution,we studied the generalized Cline's formula and generalized Jacobson's lemma for pseudo core inverse.Under the conditions of dbd=acd,bdb=bac or dbd=acd,aca=dba,the equivalent conditions for 1-bd(resp,bd)to have pseudo core inverse are discussed,when 1-ac(resp,ac)has pseudo core inverse.Furtherly,the pseudo core inverse of 1-bd(resp,bd)is given in terms of 1-ac(resp,ac).