斜Hurwitz级数环的PP性质  

PP Property of Rings of Skew Hurwitz Series

作　　者：姜侠[1] 单文鹏 

机构地区：[1]西北师范大学数学与信息科学学院 [2]兰州铁路第三中学,甘肃兰州730030

出　　处：《甘肃科学学报》2007年第1期23-25,共3页Journal of Gansu Sciences

摘　　要：研究了斜Hurwitz级数环的PP性质,证明了当R是σ-刚性环,且R关于加法做成的群是挠自由群时,R上的斜Hurwitz级数环是PP-环当且仅当R是PP-环,且R的每个由幂等元组成的可数集在R的全体幂等元组成的集合B(R)中有上确界.还证明了若R是交换的σ-刚性环,且R关于加法做成的群是挠自由群时,R上的斜Hurwitz级数环是弱PP-环当且仅当R是弱PP-环.The PP and weak PP properties of the ring of skew Hurwitz series are studied. It is proved that if R is an σ-rigid ring and the addition group of R is a torsion-free group, then the ring of skew Hurwitz series over R is a PP-ring if and only if R is a PP-ring and any countable family of idempotents of R has a least upper bound in B（R）, where B（R） is the set of all idempotents in R. It is also shown that if R is a commutative σ-rigid ring and the addition group of R is a torsion-free group, then the ring of skew Hurwitz series over R is weak PP if and only if R is weak PP.

关 键 词：斜Hurwitz级数环 σ-刚性环 PP-环 弱PP-环 

分 类 号：O153.3[理学—数学]