A domain is a non-trivial 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-trivial ring without zero divisors.
A domain is a non-trivial 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-trivial ring without zero divisors.