On existence of directly finite, only one sided self-injective regular rings

On One-Sided Ideals of Rings of Linear Transformations

On semiperfect rings of injective dimension one

We give a characterization of right Noetherian semiprime semiperfect and semidistributive rings with inj. dimAAA 6 1.

on one-sided ideals of rings of linear transformations

On One-sided Lie Nilpotent Ideals of Associative Rings

We prove that a Lie nilpotent one-sided ideal of an associative ring R is contained in a Lie solvable two-sided ideal of R. An estimation of derived length of such Lie solvable ideal is obtained depending on the class of Lie nilpotency of the Lie nilpotent one-sided ideal of R. One-sided Lie nilpotent ideals contained in ideals generated by commutators of the form [. . . [[r1, r2], . . .], rn−1...

Torsionfree Dimension of Modules and Self-injective Dimension of Rings

Let R be a left and right Noetherian ring. We introduce the notion of the torsionfree dimension of finitely generated R-modules. For any n 0, we prove that R is a Gorenstein ring with self-injective dimension at most n if and only if every finitely generated left R-module and every finitely generated right R-module have torsionfree dimension at most n, if and only if every finitely generated le...