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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?

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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

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