Integral Domain

Definition : Let R be a Ring, R is an integral domain if \forall a,b \in R such that a \neq 0 and b \neq 0 then a*b \neq 0

An integral domain is a Ring where no two nonzero elements can produce zero when multiplied. Thus integral domains do not have zero divisors. One can show that a Ring is an integral domain by showing the existence of units. An example of an integral domain is the integers since no two nonzero integer can produce zero through multiplication.

See Also : Ring, Unit, Zero Divisor

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