Meaning of reduced ring | Babel Free

Definitions

A ring R that has no nonzero nilpotent elements; equivalently, such that, for x ∈ R, x² = 0 implies x = 0.

Equivalents

Examples

“We do this for reduced rings in Corollary 10, and for rings with nonzero nilpotents in Corollary 15.”

“Extending the notion of a reduced ring, we call a right module M over a ring R a reduced module if, for any m#92;inM and a#92;inR, ma#61;0 implies mR#92;capMa#61;0. Various results of reduced rings are extended to reduced modules.”

“In general, the first case of importance is the normalization of a reduced ring R in its quotient ring K(R).”

CEFR level