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1. • CommentRowNumber1.
   • CommentAuthorHewWolff
   • CommentTimeSep 11th 2014
   • (edited Sep 11th 2014)
   • PermaLink
   Author: HewWolff
   Format: MarkdownItexI have not yet made this change -- as a newbie, I want to get an opinion first. [associative unital algebra](http://nlab.mathforge.org/nlab/show/associative+unital+algebra) describes an $R$-algebra $A$, for $R$ commutative, as a "ring under $R$". From [under category](http://nlab.mathforge.org/nlab/show/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](https://en.wikipedia.org/wiki/Algebra_%28ring_theory%29)). I'm not sure how to fix that. Maybe we should just remove the "under $R$" item from that first page. Thoughts?

   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?

2. • CommentRowNumber2.
   • CommentAuthorTodd_Trimble
   • CommentTimeSep 12th 2014
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   Author: Todd_Trimble
   Format: MarkdownItexGood 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).

   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).

3. • CommentRowNumber3.
   • CommentAuthorUrs
   • CommentTimeSep 12th 2014
   • PermaLink
   Author: Urs
   Format: MarkdownItexhave added the center clause

   have added the center clause

4. • CommentRowNumber4.
   • CommentAuthorHewWolff
   • CommentTimeSep 12th 2014
   • PermaLink
   Author: HewWolff
   Format: MarkdownItexI made a similar change in [[under category]]: I think the commutative algebras over a field $F$ are $F \downarrow$[[CRing]], not $F \downarrow$[[Ring]].

   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.

5. • CommentRowNumber5.
   • CommentAuthorUrs
   • CommentTimeSep 13th 2014
   • PermaLink
   Author: Urs
   Format: MarkdownItexOf course. Thanks a lot for catching that!

   Of course. Thanks a lot for catching that!