EMBEDDINGS OF VALUED GROUPS

摘要

In this paper we investigate the problem of embedding a valued group into an adequate Hahn group. The study of groups with general valuation - an ultramet-ric function into an ordered set with a least element - was initiated in [7].If G is a group with a normal valuation, then one can construct a Hahn product of the factor groups formed from the closed 0-centered balls over the respective open balls. Since the Hahn group consists of those elements of the general product group whose supports are dually well-ordered, its elements may be regarded as a kind of generalized sequences and thus their operational behaviour is reasonably regular. Furthermore, it is worth noting that, in most cases, the Hahn products are continuously closed and Cauchy complete; see [8].