A zero-dimensional local ring that is not a tensor product of two zero-dimensional local rings

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Does there exist a commutative unital local ring $R$ of Krull dimension $0$ such that for any two commutative unital local rings $R_1$, $R_2$ of Krull dimension $0$ we have $R\not \approx R_1\otimes_{\mathbb{Z}}R_2$?