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تسجيل مستخدم جديدRegular elements determined by generalized inverses
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In a semiprime ring, von Neumann regular elements are determined by their inner inverses. In particular, for elements $a,b$ of a von Neumann regular ring $R$, $a=b$ if and only if $I(a)=I(b)$, where $I(x)$ denotes the set of inner inverses of $xin R$. We also prove that, in a semiprime ring, the same is true for reflexive inverses.
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