2012•Journal of Nanchang UniversityRequires access

Compatibility between orderings and valuations in commutative semiring

Wan Yan-fei

Abstract

The compatibility between orderings and valuations was investigated in a commutative semiring.By introducing the notion of semisections for valuations on a commutative semiring,it proved that the valuation on a commutative semiring possesses a semisection,as long as its value monoid is a group.Based on this fact,the following main result was established:for a valuation on a commutative semiring v,is real if and only if it is compatible with some ordering of.

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Key concepts: Semiring, Commutative property, Mathematics, Valuation (finance), Pure mathematics, Discrete mathematics, Combinatorics, Business