ABSTRACT
An important role in the theory of rings and modules is played by various finiteness conditions. Many types of finiteness conditions on rings can be formulated in terms of d.c.c. (descending chain condition) or a.c.c. (ascending chain condition) on suitable classes of one-sided ideals. The d.c.c. (minimal condition) on right (left) ideals defines right (left) Artinian rings. Analogously, right (left) Noetherian rings are defined as rings which satisfy the maximal condition, or the a.c.c. on right (left) ideals. These rings were considered in [146, chapter 3].
