Can a semiring other than monosemiring posses a common neutral element with respect to both the operations defined on it?

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In general, a semiring contains two distinct identities with respect to addition and multiplication defined on it. In particular, monosemiring is the one in which the neutral element is common with respect to both the operations defined on it. I found some semiring like structures other than monosemiring in which both the operations have same neutral element.