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In abstract algebra, a semiring is an algebraic structure. Semirings are a generalization of rings, dropping the requirement that each element must have an additive inverse. At the same time, semirings are a generalization of bounded distributive lattices.
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| Subject | Predicate | Object | Confidence | Src |
|---|---|---|---|---|
| Semiring | is a | algebraic structure | 0.90 | text |
| Semiring | is a | set R | 0.90 | text |
| Semiring | is a | sub-semiring and being commutative is equivalent to being its own center.The commutative semiring of natural numbers is the initial object among its kind | 0.90 | text |
| Semiring | is a | idempotent semiring and with addition defined over arbitrary sets.An additively idempotent semiring with idempotent multiplication | 0.90 | text |
| Semiring | is a | semiring for which the additive monoid is a complete monoid | 0.90 | text |
| Semiring | is a | semiring with an additional unary operator | 0.90 | text |
| Semiring | is a | star semiring satisfying the sum-star and product-star equations | 0.90 | text |
| Semiring | is a | Conway semiring satisfying the Conway group axioms | 0.90 | text |
| Semiring | is a | semiring isomorphic to a sub-semiring of a Boolean algebra.The commutative semiring formed by the two-element Boolean algebra and defined by 1 | 0.90 | text |
| Semiring | is a | empty set | 0.90 | text |
| commutativity simplify the axioms.Given a strict total order | instance of | Additional properties | 0.80 | text |
| Semiring | has application | The | 0.60 | section |
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