关于产品$ac$和$ba$共同性质的注记
Remark on common properties of the products $ac$ and $ba$
摘要：
本文讨论了在$a(ba)^{2}=abaca=acaba=(ac)^{2}a$条件下各种范畴积$ac$和$ba$的共同性质。证明了广义Jacobson引理和Cline公式适用于环上的广义n-强Drazin可逆算子，广义Jacobson引理适用于巴拿赫空间上的左、右弗雷德霍姆算子.
英文摘要：
In this paper, we discuss the common properties for the products $ac$ and $ba$ in various categories under the condition $a(ba)^{2}=abaca=acaba=(ac)^{2}a$. We prove that generalized Jacobson's lemma and Cline's formula are suitable for generalized n-strong Drazin invertible in rings, and generalized Jacobson's lemma is suitable for left and right Fredholm operator on Banach spaces.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
