Valuations and real valuations on semiring
Wan Yan-fei · Journal of Nanchang University · 2011
The notions of valuations and real valuations were introduced in the category of commutative semirings with units.Some basic results on valuations and real valuations of semirings were derived.Moreover,the compatibility between preorderings and valuations was analyzed for a commutative semirings.It also proved that a valuation,as a necessary and sufficient condition,is real if and only if it is compatible with some preordering.