The difference between Domain and Integral domain
When used as nouns, domain means a geographic area owned or controlled by a single person or organization, whereas integral domain means any nonzero commutative ring in which the product of nonzero elements is nonzero.
check bellow for the other definitions of Domain and Integral domain
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Domain as a noun:
A geographic area owned or controlled by a single person or organization.
Examples:
"The king ruled his domain harshly."
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Domain as a noun:
A field or sphere of activity, influence or expertise.
Examples:
"Dealing with complaints isn't really my domain: get in touch with customer services."
"His domain is English history."
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Domain as a noun:
A group of related items, topics, or subjects.
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Domain as a noun (mathematics):
The set of all possible mathematical entities (points) where a given function is defined.
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Domain as a noun (mathematics, set theory):
The set of input (argument) values for which a function is defined.
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Domain as a noun (mathematics):
A with no zero divisors; that is, in which no of nonzero elements is zero.
Examples:
"hyponyms integral domain"
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Domain as a noun (mathematics, topology, analysis):
An open and connected set in some topology. For example, the interval (0,1) as a subset of the real numbers.
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Domain as a noun (computing, Internet):
Any DNS domain name, particularly one which has been delegated and has become representative of the delegated domain name and its subdomains.
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Domain as a noun (computing, Internet):
A collection of DNS or DNS-like domain names consisting of a delegated domain name and all its subdomains.
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Domain as a noun (computing):
A collection of information having to do with a domain, the computers named in the domain, and the network on which the computers named in the domain reside.
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Domain as a noun (computing):
The collection of computers identified by a domain's domain names.
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Domain as a noun (physics):
A small region of a magnetic material with a consistent magnetization direction.
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Domain as a noun (computing):
Such a region used as a data storage element in a bubble memory.
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Domain as a noun (data processing):
A form of technical metadata that represent the type of a data item, its characteristics, name, and usage.
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Domain as a noun (taxonomy):
The highest rank in the classification of organisms, above kingdom; in the three-domain system, one of the taxa Bacteria, Archaea, or Eukaryota.
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Domain as a noun (biochemistry):
A folded section of a protein molecule that has a discrete function.
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Integral domain as a noun (algebra, ring theory):
Any nonzero commutative ring in which the product of nonzero elements is nonzero.
Examples:
"A ring <math>R</math> is an integral domain if and only if the polynomial ring <math>R[x]</math> is an integral domain."
"For any integral domain there can be derived an associated [[field of fractions]]."