A ring R is a left qpring if
each of its left ideals is quasiprojective as a left Rmodule in the sense of
Wu and Jans. The following results giving the structure of left qprings are
obtained. Throughout R is a perfect ring with radical N: (1) Let R be local.
Then R is a left qpring iff N^{2} = (0) or R is a principal left ideal ring with
dcc on left ideals, (2) If R is a left qpring and T is the sum of all those
indecomposable left ideals of R which are not projective, then T is an ideal of R
and N = T ⊕ L, L is a left ideal of R such that every left subideal of L is
projective, R∕T is hereditary, and R is heredity iff T = (0). (3) If R is left
qpring then R = , where S is hereditary, T is a direct sum of
finitely many local qprings and M is a (S,T)bimodule. (4) A perfect left
qpring is semiprimary. (5) Let R be an indecomposable ring such that it
admits a faithful projective injective left module. Then R is a left qpring iff
R is a local principal left ideal ring or R is a lefthereditary ring with dcc
on left ideals. (6) Let R be an indecomposable QFring. Then R is a left
qpring if each homomorphic image of R is a qring (each onesided ideal
is quasiinjective). (7) If a left ideal A of left qpring R is not projective
then the projective dimension of A is infinite, thus lgl.dimR = 0,1, or ∞.
An example of a left artinian left qpring which is not right qpring is also
given.
