Talk:Tensor product of algebras

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You have mentioned that for Z-Algebras (or commutative rings) the canonical mapping A -> A @_R B and B -> A @_R B are injections, why is this so?

Sincerely Jose

Well, that may not be true, I think. I have made it 'homomorphisms'. Charles Matthews 15:16, 4 April 2007 (UTC)

No they aren't, there is an example.. for instance Q @_Z Z_p ... for the Z-algebras Q and Z_p,

1@x = 0@0 for any x in Z_p (since 1@x=1/p@xp=1/p@0 ), thus Z_p is not an injection into Q @_Z Z_p

But if A and B were R overrings, then I think this could lead into injections.. I need to look up some homological algebra which I have almost 0 knowledge in.

Sincerely, Jose