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purpose of disambiguation, one may write or to emphasize which structure the units at hand belong to.

If is an element of a semiring and , then -times repeated multiplication of with itself is denoted , and one similarly writes for the -times repeated addition.

Construction of new semirings

The zero ring with underlying set is a semiring called the trivial semiring. This triviality can be characterized via and so when speaking of nontrivial semirings, is often silently assumed

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