A proof of a conjecture of Vandiver
I. N. Herstein · Proceedings of the American Mathematical Society · 1950
The Wedderburn theorem that every finite division ring is commutative has been extended by several authors [1].1 Vandiver, in his paper The p-adic representation of rings [2 ] conjectured the following generalization of Wedderburn's theorem: every finite, non-commutative ring contains an element which is a divisor of zero and is not in the centrum. In this paper we give a short and simple proof of this conjecture. We also exhibit one generalization of it which was pointed out to us by the referee.