# Integral Domain12

Every prime ideal in a Boolean ring is maximal
A finite unital ring with no zero divisors is a field
The ideal generated by the variable is maximal iff the coefficient ring is a field
Prove that a given quotient ring is not an integral domain
If a nontrivial prime ideal contains no zero divisors, then the ring is an integral domain
In an integral domain, two principal ideals are equal precisely when their generators are associates
In a polynomial ring, the ideal generated by the indeterminate is prime precisely when the coefficient ring is an integral domain
The characteristic of an integral domain is prime or zero
The ring of formal power series over an integral domain is an integral domain
The only Boolean integral domain is Z/(2)