In this post, I’d like to record a few basic definitions and results regarding noncommutative rings. This is a subject clearly of great importance and generality, but I haven’t had much exposure to it, and I’m trying to fix that. I am working mostly from Lam’s A first course in noncommutative rings.
Archive for January, 2012
Here’s what seems like a silly question: what’s the universal group? That is, what’s the universal example of a set together with maps
satisfying the identities
A moment’s reflection shows that there isn’t such a group; the existence of the groups , where is an arbitrary set, shows that there exist groups of arbitrarily large cardinality, so no particular group can be universal.