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)

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)

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)

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

Link to the orphan page

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

http://en.wikipedia.org/wiki/Example_of_a_non-associative_algebra 131.220.107.25 (talk) 16:58, 24 March 2011 (UTC)

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)

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

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)

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