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Domains are useful in many fields of mathematics, including the study of [[analytic]] and [[harmonic functions]].
Domains are useful in many fields of mathematics, including the study of [[analytic]] and [[harmonic functions]].
[[category:mathematics]]
[[Category:Mathematics]]
In algebra, a domain is a [[commutative]] [[ring (mathematics)|ring]] <math>R</math> with identity <math>1 \neq 0</math> without zero divisors: that is, for every <math>a, b \in R</math>, if <math>ab = 0</math>, then <math>a = 0</math> or <math>b = 0</math>.
In algebra, a domain is a [[commutative]] [[ring (mathematics)|ring]] <math>R</math> with identity <math>1 \neq 0</math> without zero divisors: that is, for every <math>a, b \in R</math>, if <math>ab = 0</math>, then <math>a = 0</math> or <math>b = 0</math>.