Opposite of a Semiring

The opposite semiring of a Semiring R 𝑅 R is a Semiring R m ⁢ a ⁢ t ⁢ h ⁢ r ⁢ m ⁢ o ⁢ p superscript 𝑅 𝑚 𝑎 𝑡 ℎ 𝑟 𝑚 𝑜 𝑝 R^{mathrm{op}} whose additive monoid is the additive monoid of R 𝑅 R , and multiplicative monoid is the Opposite of the multiplicative monoid of R 𝑅 R .