Talk:Algebra (ring theory)

Page should address nonassociative algebras

There is a separate page for associative algebras. This article should be merged with associative algebra or expanded to include the nonassociative types. —Preceding unsigned comment added by 67.84.223.89 (talk) 02:28, 21 August 2009 (UTC)[reply]

merging old article with associative algebra

The merge is in process right now. Please don't revert until it is finished —Preceding unsigned comment added by 67.194.131.154 (talk) 14:51, 6 September 2009 (UTC)[reply]

The definition should include noncommutative algebras

The more general definition is shorter and easier to state. —Preceding unsigned comment added by MephJones (talk • contribs) 21:12, 12 March 2010 (UTC)[reply]

I take it you haven't read the article yet. Sławomir Biały (talk) 19:39, 1 May 2010 (UTC)[reply]

Link to the orphan page

Help this little guy out, he's all alone in the world:

http://en.wiki.x.io/wiki/Example_of_a_non-associative_algebra 131.220.107.25 (talk) 16:58, 24 March 2011 (UTC)[reply]

Question

Given a commutative ring R, when is it true that every ring homomorphism $f\colon R\to S$ with domain R realizes S as an R-algebra? Is it equivalent to the unique homomorphism $\mathbb {Z} \to R$ being an epimorphism in the category of rings? GeoffreyT2000 (talk) 22:44, 12 April 2015 (UTC)[reply]

The image should lie in the center of S and that's also a sufficient condition. -- Taku (talk) 04:12, 30 April 2015 (UTC)[reply]

More generally, this statement generalizes to monoids in any cosmos with monic coproduct injections. A cosmos is a complete cocomplete symmetric closed monoidal category. GeoffreyT2000 (talk) 22:58, 5 May 2015 (UTC)[reply]

I am talking about every homomorphism with domain R, not a particular one. GeoffreyT2000 (talk) 17:24, 10 May 2015 (UTC)[reply]