Tensor product with any Noetherian integral domain is Noetherian

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Let $k$ be a field. Algebras are assumed to be commutative, associative, unital. If for a $k$-algebra the $k$-tensor product with any Noetherian integral domain over $k$ is Noetherian, is the $k$-tensor product with any Noetherian $k$-algebra Noetherian?