that if R is α-rigid then R is PP ring if and only if R[x;α,δ] is PP ring.

Ore extensions of weakly GPP-rings;

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.

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,under the same conditions,R*((G)) is a weakly PP-ring if and only if R is a weakly PP-ring.

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).