广义几乎有限值l-群的结构

THE STRUCTURE OF GENERAL ALMOST FINITE-VALUED l-Groups

l-群G称为广义几乎有限值的 ,如果对于 0≠g∈G ,g除了w(可数 )个非特殊值外 ,其余均是特殊值。此时称 g是G的w -特殊元 ,g的w个非特殊值称为G的w -特殊值。本文的主要结果是 :G是l -群 ,以下条件彼此等价。 1)G∈Fυw(广义几乎有限值l-群类 ) ;2 )G的每个值是特殊的或w -特殊的 ;3)对于 0 <g∈G ,g可表为有限个分离w -特殊元的和。当w =0时 ,即Conrad[1] 中的定理 3.9,当w =n(自然数 ) ,即是Martinez[2 ]

An l-group G is said to be general almost finite-valued l-group,if for each 0≠g∈G every value of g except for w,is special.g is said to be w-special element and every non-special value of g is said to be w-special value.The main result of this paper is the following statement.Let G be an l-group,the following conditions are equivalent.1) G∈F υ w ;2) Each value of G is special or w-special;3) Each 0<g≤G can be written as a sum of pairwise disjoint w-special elements.