Yanxun Ren

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math.RA2021

Remark on common properties of the products $a c$ and $ba$

Yanxun Ren, Lining Jiang

In this paper, we discuss the common properties for the products $a c$ and $ba$ in various categories under the condition $a (ba)^{2} = aba c a = a c aba = (a c)^{2} a$ . We prove that generalize…

math.RA2021

Extensions of Jacobson's lemma for generalized inverses in a ring

Yanxun Ren, Lining Jiang

Let $R$ be an associative ring with unit $1$ , and $a, b, c \in R$ satisfy $a (ba)^{2} = aba c a = a c aba = (a c)^{2} a$ , this paper proves that $1 - a c$ has generalized Drazin inverse (Drazin inv…

Remark on common properties of the products ac and ba

Extensions of Jacobson's lemma for generalized inverses in a ring

Remark on common properties of the products $a c$ and $ba$