5

Let $A$ be a finite unital ring and let $N$ be the set of nonunits of $A$. I want to show that if $|N|>1$ then $\sqrt{|A|}\leq |N|$. I have tried to find an injective function from $A$ to $N$, but I don't know anything about whether $A$ is commutative or not.

Matemáticos Chibchas
  • 6,271
user194502
  • 111

1 Answers1

1

Note that every left or right divisor in your ring is a nonunit. Now follow the reasoning of this paper. Don't get afraid, the argument is quite elementary.

Matemáticos Chibchas
  • 6,271