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I have not yet made this change – as a newbie, I want to get an opinion first.
associative unital algebra describes an $R$-algebra $A$, for $R$ commutative, as a “ring under $R$”. From under category, this is just an object in the coslice category $R \downarrow \operatorname{Ring}$: a map $R \to A$, where $A$ is another ring. However, I believe that such a map gives an $R$-algebra only if its image is in the center of $A$ (for example, Wikipedia). I’m not sure how to fix that. Maybe we should just remove the “under $R$” item from that first page. Thoughts?
Good catch. Probably whoever wrote it was remembering this description for commutative algebras $A$.
I agree this description should be removed; please be our guest (and thanks).
have added the center clause
I made a similar change in under category: I think the commutative algebras over a field $F$ are $F \downarrow$CRing, not $F \downarrow$Ring.
Of course. Thanks a lot for catching that!
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