What does principal ideal domain mean?
Definitions for principal ideal domain
prin·ci·pal ide·al domain
This dictionary definitions page includes all the possible meanings, example usage and translations of the word principal ideal domain.
Wiktionary
principal ideal domainnoun
An integral domain in which every ideal is a principal ideal.
Wikidata
Principal ideal domain
In abstract algebra, a principal ideal domain, or PID, is an integral domain in which every ideal is principal, i.e., can be generated by a single element. More generally, a principal ideal ring is a nonzero commutative ring whose ideals are principal, although some authors refer to PIDs as principal rings. The distinction is that a principal ideal ring may have zero divisors whereas a principal ideal domain cannot. Principal ideal domains are thus mathematical objects which behave somewhat like the integers, with respect to divisibility: any element of a PID has a unique decomposition into prime elements; any two elements of a PID have a greatest common divisor. If x and y are elements of a PID without common divisors, then every element of the PID can be written in the form ax + by. Principal ideal domains are noetherian, they are integrally closed, they are unique factorization domains and Dedekind rings. All Euclidean domains and all fields are principal ideal domains.
Numerology
Chaldean Numerology
The numerical value of principal ideal domain in Chaldean Numerology is: 5
Pythagorean Numerology
The numerical value of principal ideal domain in Pythagorean Numerology is: 5
Translations for principal ideal domain
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- 単項イデアルドメインJapanese
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"principal ideal domain." Definitions.net. STANDS4 LLC, 2024. Web. 13 May 2024. <https://www.definitions.net/definition/principal+ideal+domain>.
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