Ian Payne, Department of Pure Mathematics, University of Waterloo
“Normal Subgroups, Ideals, and Kernels”
Normal subgroups of groups and ideals of rings seem to play the same role: you can quotient by them. More precisely, they induce equivalence relations on their domain by which you can quotient. I’ll talk about just enough universal algebra to explain which equivalence relations give well defined quotients in a more general setting. Once that is done, I’ll use an example from groups to try to convince you that studying these equivalence relations is worthwhile.