2 theorem of jacobson and rickart part 1

The first part of the proof of a theorem of Jacobson and Rickart which shows that a Jordan homomorphism between two associative rings $A$ and $B$ is either an associative homomorphism or anti-homomorphism under the assumption that $B$ has no zerodivisors.

In this first half, we show that for every two elements $a, b \in A$, we either have $\sigma(ab) = \sigma(a)\sigma(b)$ or $\sigma(ab) = \sigma(b)\sigma(a)$, where $\sigma: A \to B$ is the Jordan homomorphism.

[haggaisimon]

In general, nice lectures. A bit old fashioned since Jacobson book may be outdated.