In this thesis, we mainly investigate several general injective modules, general pp rings, and the relationships between them.

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.

The purpose of this paper is to investigate the so-called multiplicatively directed families of ideals and their generalized quotient rings.

It is given in this paper that the polynomial rings on R are sufficient conditions of generalized Hopfian,and an example of generalized Hopfian ring of direct product R×S is also constructed.