- #1
mathmari
Gold Member
MHB
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Hey! ![Eek! :eek: :eek:](data:image/gif;base64,R0lGODlhAQABAIAAAAAAAP///yH5BAEAAAAALAAAAAABAAEAAAIBRAA7)
Let $R$ be a finite non-trivial ring.
We suppose that for each $r,s\in R$ with $rs=0$ then either $r=0$ or $s=0$.
I want to show that $R$ is a division ring.
Could you give me a hint how we could show that each element $x\in R\setminus \{0\}$ has an inverse? (Wondering)
Let $R$ be a finite non-trivial ring.
We suppose that for each $r,s\in R$ with $rs=0$ then either $r=0$ or $s=0$.
I want to show that $R$ is a division ring.
Could you give me a hint how we could show that each element $x\in R\setminus \{0\}$ has an inverse? (Wondering)