Semiring
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High Quality Content by WIKIPEDIA articles! High Quality Content by WIKIPEDIA articles! In abstract algebra, a semiring is an algebraic structure similar to a ring, but without the requirement that each element must have an additive inverse. The term rig is also used occasionally this originated as a joke, suggesting that rigs are rings without negative elements. This last axiom is omitted from the definition of a ring: it follows automatically from the other ring axioms. Here it does not, and it is necessary to state it in the definition. The difference between rings and semirings, then, is…mehr

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High Quality Content by WIKIPEDIA articles! High Quality Content by WIKIPEDIA articles! In abstract algebra, a semiring is an algebraic structure similar to a ring, but without the requirement that each element must have an additive inverse. The term rig is also used occasionally this originated as a joke, suggesting that rigs are rings without negative elements. This last axiom is omitted from the definition of a ring: it follows automatically from the other ring axioms. Here it does not, and it is necessary to state it in the definition. The difference between rings and semirings, then, is that addition yields only a commutative monoid, not necessarily a commutative group. Specifically, elements in semirings do not necessarily have an inverse for the addition.