Semiring

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Related to Idempotent semiring: semiring of sets

Sem´i`ring`

(sĕm´ĭ`rĭng`)

(Anat.) One of the incomplete rings of the upper part of the bronchial tubes of most birds. The semirings form an essential part of the syrinx, or musical organ, of singing birds.

Webster's Revised Unabridged Dictionary, published 1913 by G. & C. Merriam Co.

References in periodicals archive ?

(1) (NSS[(U).sup.E], [[union].sub.R], [[intersection].sub.R]) is a commutative, idempotent semiring with [[union].sub.E] as an identity element.

(2) (NSS[(U).sup.E], [[union].sub.R], [[intersection].sub.E]) is a commutative, idempotent semiring with [[PHI].sub.[PHI]] as an identity element.

(7) (NSS[(U).sup.E], [[union].sub.E], [[intersection].sub.R]) is a commutative, idempotent semiring with [[PHI].sub.E] as an identity element.

Algebraic structures of neutrosophic soft sets

The semiring is said to be an idempotent semiring if the two reducts are bands, that is, semirings where every element is an idempotent.

Zhao, Green's D-relation for the multiplicative reduct of an idempotent semiring, Arch.

Keywords Idempotent semirings; Subdirect product; Variety; Congruence.

Suppose V is a subvariety of I, we denote by [??] the variety of all idempotent semirings S in which the multiplicative reduct (S; *) of S belongs to V.

Zhao, Varieties of idempotent semirings with a commutative addition, Algebra Universal, to appear.

Shum, D-subvariety of idempotent semirings, Algebra Colloquium, 9 (2002), 15-28.

On a subvariety of [??]

Axioms (1)-(11) say that the structure is an idempotent semiring under +, [center dot], 0, and 1, and the remaining axioms (12)-(17) say essentially that * behaves like the Kleene star operator of formal language theory or the reflexive transitive closure operator of relational algebra.