Difference between revisions of "Domain"
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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]]. | ||
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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>. | ||
Latest revision as of 11:45, July 13, 2016
A domain is the set of points where a mathematical function is defined. When the function is a function of a complex variable, a domain is usually an open connected set.
Domains are useful in many fields of mathematics, including the study of analytic and harmonic functions.
In algebra, a domain is a commutative ring with identity without zero divisors: that is, for every , if , then or .
