带扭结的广义幂级数环的特殊性质  

Special properties of rings of twisted generalized power series

作　　者：严兴凤[1] 

机构地区：[1]西北师范大学数学与信息科学学院,甘肃兰州730070

出　　处：《西北师范大学学报（自然科学版）》2007年第2期20-23,共4页Journal of Northwest Normal University(Natural Science)

摘　　要：考虑带扭结的广义幂级数环[[Rs,≤,λ]]的一些特殊性质.证明了[[Rs,≤,λ]]是reduced左PP-环当且仅当R是reduced左PP-环,且B(R)的每个S可标子集C在B(R)中有最小上界;若环R无非零零因子,则[[Rs,≤,λ]]是Dedekind有限环当且仅当R是Dedeking有限环.The special properties of the ring [[R^s,≤,λ]] of twisted generalized power series are discussed. It is proved that the ring [[R^s,≤,λ]] is a reduced left PP-ring if and only if R is a reduced left PP-ring and every S-indexed subset C of B（R） has a least upper bound in B（R）~;R is a ring without nonzero zerodivisors, then the ring [[R^s,≤,λ]] ts Dedeking finite if and only if R is Dedeking finite.

关 键 词：带扭结的广义幂级数环 PP-环 Dedekind有限环 

分 类 号：O153.3[理学—数学]