TITLE: Morita equivalence of $K$-algebras
QUESTION [5 upvotes]: 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?

REPLY [2 votes]: 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