关于正规值l-群的几个注记

Some Notes on Normal-valued l-groups

研究了正规值l-群的几个性质:①G是正规值l-群,0<g∈G,则M∈ValG(g)当且仅当对于坌0<a∈M,a是g的下元,对于坌0<b埸M,b不是g的下元;②G是l-群,则G是离散的当且仅当G是正规值的,且对于坌g∈G+,存在G的特殊元a,使得g≥a,且a的唯一值是极小素的.

The authors some properties of normal-valued l-groups in this paper : (1) Let G be a normal-valued l-group and 0<g∈G. Then M∈ValG(g) if and only if 0<a∈G, a is a blow element of g, and for any 0<b∈M, b is not a below element of g ;(2) Let G be a l-group. Then G is discreet if and only if G is normal-valued and for any g∈G+ ,there exists a special element a so that g≥a and the unique value of is minimal prime.