Consider a right ideal L in a
ring (with 1 ∈ R or 1∉R), its idealizer N = {n ∈ R|nL ⊆ L}, the bound
P = {r ∈ L|Rr ⊆ L} ⊲ R of L, and the ideal H = {n ∈ N|nL ⊆ P} ⊲ N. II.
Some of the ideal structure of the ring N∕P is determined for a class of
one sided prime ideals L more general than the almost maximal ones and
without any chain conditions on R (Theorem II). III. When L≠P the following
conditions are necessary and sufficient for N∕P to have precisely two unequal,
nonzero minimal prime ideals L∕P and H∕P: (i) H≠P; (ii) L∕P < R∕P is not
essential; (iii) L∕P is a maximal annihilator in R∕P; (iv) the left annihilator
of L∕P is not zero; (v) L = {r ∈ R|ur ∈ P} for some u ∈ N∖L (Theorem
III).
