Page "Boolean ring" Paragraph 22

A map between two Boolean rings is a ring homomorphism if and only if it is a homomorphism of the corresponding Boolean algebras.

Furthermore, a subset of a Boolean ring is a ring ideal ( prime ring ideal, maximal ring ideal ) if and only if it is an order ideal ( prime order ideal, maximal order ideal ) of the Boolean algebra.

The quotient ring of a Boolean ring modulo a ring ideal corresponds to the factor algebra of the corresponding Boolean algebra modulo the corresponding order ideal.