Stable subsets of modules and the existence of a unit in associative ringsстатья
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Дата последнего поиска статьи во внешних источниках: 8 апреля 2022 г.
Аннотация: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.
Key words
quasiunitary module quasiunitary ring stable set of a ring stabilizer balanced set idempotent central idempotent unit left unit