环上的Baer-Krull定理Ⅱ

THE BAER-KRULL THEOREM FOR COMMUTATIVE RINGS Ⅱ

在半序的支集与赋值的核未必相等的一般情形下,研究了交换环上半序的结构,是文献[1]的继续。通过引入模上半序这一概念,建立了一些结果,这些结果揭示了交换环中与给定赋值相容的半序(和序)的结构。作为推论,一个形式更一般的Baer-Krull定理被推广到交换环上。

This paper is a continuation of reference[1].The purpose of this paper is to investigate the structure of semiorderings (and orderings) of a ring in the general case when the supports of the considered semiorderings need not be coincident with the core of their compatible valuation.By introducing the concept of semiorderings on a module,some results on the structure of semiorderings(and orderings) compatible with a given valuation are obtained.As an important consequence,a general version of Baer-Krull theorem is established in the category of commutative rings.