Published online by Cambridge University Press: 09 April 2009
In this paper the structure of rings with dual continuous right ideals is discussed. The main result is the following: If R is a ring with (Jacobson) radical nil, and all of its finitely generated right ideals are dual continuous, then where S is a finite direct sum of local rings each of which has its radical square zero, or is a right valuation ring, T is semiprimary right semihereditary ring, and M is an (S, T)-bimodule such that all of its finitely generated T-submodules are projective. A partial converse of this result is obtained: any matrix ring of the above type with M = 0 has all of its finitely generated right ideals dual continuous.