Definition 1. A domain is a non-zero ring $R$ such that for all $a$, $b \in R$,
\[ab = 0 \enspace\rimp\enspace a = 0 \,\lor\, b = 0.\]In other words, a domain is a non-zero ring without zero divisors.
Not to be confused with domain of a relation!
Pub Apr 05, 2026 Up Jun 11, 2026
Not to be confused with domain of a relation!
Definition 1. A domain is a non-zero ring $R$ such that for all $a$, $b \in R$,
\[ab = 0 \enspace\rimp\enspace a = 0 \,\lor\, b = 0.\]In other words, a domain is a non-zero ring without zero divisors.