5
$\begingroup$

Given $K$ a unital commutative ring and $A$ a $K$-algebra different from $K$. Can $K$ be Morita equivalent to $A \amalg A$, where $A \amalg A$ is the coproduct in the category of unital associative $K$-algebras?

$\endgroup$

1 Answer 1

2
$\begingroup$

If V is a vector space such that $V\oplus V$ is isomorphic to V then A=TV, the tensor álgebra, is isomorphic to $T(V\oplus V)=A\coprod A$, in particular Morita equivalent

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Not the answer you're looking for? Browse other questions tagged or ask your own question.