论文标题
戒指中的广义周
Generalized Zhou inverses in rings
论文作者
论文摘要
我们介绍并研究了环中的一类新的广义倒置。如果存在$ b \ in r $，则一个元素$ a $ in RING $ r $已概括为unverse，以至于$ bab = b，b \ in Comm^2（a），a^n-ab \ in \ sqrt {j（r）} $ in {\ bbb n} $。我们证明，r $中的$ a \ in comm^2（a）$ in Comm^2（a）$ in Complean clastermized eflesse contryperse，因此$ a^n-p \ in \ sqrt {j（r）} $ in {\ bb n} $中的某些$ n \。 Cline的公式和Jacobson的通用Zhou插座的引理已建立。特别是，表征了环中的周。
We introduce and study a new class of generalized inverses in rings. An element $a$ in a ring $R$ has generalized Zhou inverse if there exists $b\in R$ such that $bab=b, b\in comm^2(a), a^n-ab\in \sqrt{J(R)}$ for some $n\in {\Bbb N}$. We prove that $a\in R$ has generalized Zhou inverse if and only if there exists $p=p^2\in comm^2(a)$ such that $a^n-p\in \sqrt{J(R)}$ for some $n\in {\Bbb N}$. Cline's formula and Jacobson's Lemma for generalized Zhou inverses are established. In particular, the Zhou inverse in a ring is characterized.
