Michael Kinyon

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math.RA2026

Rings with finitely many zero divisors

Michael Kinyon

We give an elementary proof of a result which is not as well known as it should be: a ring with a specified finite number of zero divisors is finite, with a precise bound on its or…

math.RA2026

Elementary proofs of ring commutativity theorems

Michael Kinyon, Desmond MacHale

Jacobson's commutativity theorem says that a ring is commutative if, for each $x$ , $x^{n} = x$ for some $n > 1$ . Herstein's generalization says that the condition can be weakened to…