Algebra learning seminar

Billy Lee, Department of Pure Mathematics, University of Waterloo

“Commutativity Theorems”

This week, we will explore numerous conditions a ring may have that forces it to be a commutative ring. In particular, we will examine powerful theorem, such as “A finite division ring is a commutative field” (Wedderburn), ”If for all a in R, there exists n > 1 such that an = a then R is commutative” (Jacobson) and ”If R is semisimple, then it is commutative”.