| Abstract: | We obtain criteria for the existence of a (left) unit in rings (arbitrary, Artinian, Noetherian, prime, and so on) that are
based on the systematic study of properties of stable subsets of modules and their stabilizers that generalize the technique
of idempotents. We study a class of quasiunitary rings that is a natural extension of classes of rings with unit and of von
Neumann (weakly) regular rings, which inherits may properties of these classes. Some quasiunitary radicals of arbitrary rings
are constructed, and the size of these radicals “measures the probability” of the existence of a unit.
Translated fromMatematicheskie Zametki, Vol. 61, No. 4, pp. 596–611, April, 1997.
Translated by A. I. Shtern |
