σ ring

This article does resarch on the relationship between these classes of set,sush as field,semi-field,ring,σ field,σ ring,λ class,π class,so a further research can be done on the modern Math.

集类运算是现代数学的基础 ,特别是对一些重要集类的认识极为重要 ,本文研究了域、半域、环、σ域、σ环、λ类、π类等几个重要集类间的相互关系 ,从而可深化对现代数学的研究。

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.

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。