The singular ideal and radicals

Abstract

Some properties of the singular ideal are established. In particular its behaviour when passing to one-sided ideals is studied. Obtained results are applied to study some radicals related to the singular ideal. In particular a radical S such that for every ring R, S(R) and R/S(R) are close to being a singular ring and a non-singular ring, respectively, is constructed.

On some questions related to Koethe's nil ideal problem

“…Let R be the subalgebra ( We now obtain some results related to Problem 1.5. We shall need the following lemma, which slightly generalizes [4,Lemma 3.11] and can be obtained by applying essentially the same arguments. Proof .…”