Jonathan S. Golan, Huaxiong Wang
Abstract
We prove that every additively-idempotent semiring can be embedded in a finitary complete semiring. From this we obtain, among other results, that the classical identities of Kleene semirings over idempotent semirings are independent.
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We prove that every additively-idempotent semiring can be embedded in a finitary complete semiring. From this we obtain, among other results, that the classical identities of Kleene semirings over idempotent semirings are independent.
Key concepts: Semiring, Idempotence, Finitary, Kleene algebra, Mathematics, Embedding, Algebra over a field, Pure mathematics