1) weakly PP-ring
弱PP-环
1.
It is also shown that,under the same conditions,R*((G)) is a weakly PP-ring if and only if R is a weakly PP-ring.
在上述条件下,R*((G))是弱PP-环当且仅R是弱PP-环。
2) PP ring
PP环
1.
that if R is α-rigid then R is PP ring if and only if R[x;α,δ] is PP ring.
CHANYong-hong等证明了:假如R是α-rigid环,那么R是PP环当且仅当R[x;α,δ]是PP环。
3) PP-ring
PP-环
1.
Ore extensions of weakly GPP-rings;
弱GPP-环的Ore扩张
2.
It is proved that the ring [[Rs,≤,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 zero-divisors,then the ring [[Rs,≤,λ]] is Dedeking finite if and only if R is Dedeking finite.
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。
3.
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。
4) Almost PP ring
几乎PP环
5) right YJ-pp ring
右YJ-pp环
1.
Moreover,we show that: Every left YJ-morphic ring is a right YJ-injective ring;Every right YJ-morphic Bear ring is a right YJ-pp ring;If R is a left YJ-morphic ring,then Soc(RR) Soc(RR) and J(R)=Z(RR).
说明了以下主要结果:每一个左YJ-morphic环是右YJ-内射环;每一个右YJ-morphic的Bear环是右YJ-pp环;若R是左YJ-morphic环,则J(R)=Z(RR),Soc(RR)Soc(RR)。
6) G~*PP ring
G~*PP环
补充资料：弱弱联合
弱弱联合是指两个总体实力都不强但都拥有自己独特的某方面优势的企业之间进行联合，以形成较强的实力。弱弱联合，弱企业之间优势互补，可以形成整体实力变强的效应。
说明：补充资料仅用于学习参考，请勿用于其它任何用途。
参考词条