半环中赋值与序的相容性

Compatibility between orderings and valuations in commutative semiring

在交换半环范畴中,研究赋值与序之间的相容性。通过引进赋值的半截口,这样一个事实被证明:半环的一个赋值具有一个半截口,只要该赋值的值幺半群是一个群。基于此事实,建立了如下主要结果:对于半环S的一个赋值v,v是S的一个实赋值当且仅当v与S的某个序相容。

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 valu- ation 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.