Книга: Quasiregular Element: Mathematics, Jacobson Radical, Ring Theory, Algebraic Structure, Nilpotent, Matrix Ring, Bounded Operator, Principal Ideal, Polynomial, Unit (Ring Theory), Idempotence

High Quality Content by WIKIPEDIA articles! In mathematics, specifically ring theory, the notion of quasiregularity provides a computationally convenient way to work with the Jacobson radical of a ring. Intuitively, quasiregularity caputures what it means for an element of a ring to be 'bad' that is, have undesirable properties.[2] Although a 'bad element' is necessarily quasiregular, quasiregular elements need not be 'bad,' in a rather vague sense. In this article, we primarily concern ourselves with the notion of quasiregularity for unital rings. However, one section is devoted to the theory of quasiregularity in non-unital rings, which constitutes an important aspect of noncommutative ring theory.