A first blog post on noncommutative rings

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.

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A less biased definition of a group

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 [...]

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