Unique factorization domain：Unique Factorization Domain

Unique Factorization Domain

Auniquefactorizationdomain,calledUFDforshort,isanyintegraldomaininwhicheverynonzerononinvertibleelementhasauniquefactorization,i.e., ...。其他文章還包含有：「Lecture11」、「Noncommutativeuniquefactorizationdomain」、「NOTESONUNIQUEFACTORIZATIONDOMAINSAlfonso...」、「Section45」、「Uniquefactorizationdomain」、「uniquefactorizationdomaininnLab」、「UniqueFactorizationDomains」、「唯一分解整環」...

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Auniquefactorizationdomain,calledUFDforshort,isanyintegraldomain[1]inwhicheverynonzerononinvertibleelementhasauniquefactorization[2],i.e.,anessentiallyunique[3]decompositionastheproductofprimeelements[4]orirreducibleelements[5].Inthiscontext,thetwonotionscoincide,sinceinauniquefactorizationdomain,everyirreducibleelement[6]isprime,whereastheoppositeimplicationistrueineverydomain.Thisdefinitionarisesasanapplicationofthefundamentaltheoremofarithmetic[7],whichistrueintheringofintegers,tomoreabst...

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Lecture 11

https://acikders.ankara.edu.tr

Motiveted the unique factorization into primes (irreducibles) in Z, we investigate the integral domains which have this property. Definition. Let R be a ...

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Noncommutative unique factorization domain

https://en.wikipedia.org

In mathematics, a noncommutative unique factorization domain is a noncommutative ring with the unique factorization property.

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NOTES ON UNIQUE FACTORIZATION DOMAINS Alfonso ...

https://www.math.toronto.edu

We say that R is a unique factorization domain or. UFD when the following two conditions happen: • Every a ∈ R which is not zero and not a unit ...

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Section 45

https://jupiter.math.nycu.edu.

In general, if an integral domain has the unique factorization property, we say it is a unique factorization domain (UFD). • If an integral domain has the ...

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Unique factorization domain

https://en.wikipedia.org

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unique factorization domain in nLab

https://ncatlab.org

A principal ideal domain (PID) is a UFD. (In particular, a Euclidean domain is a UFD.) As a partial converse, a Dedekind domain that is a UFD is a PID.

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Unique Factorization Domains

https://www.jstor.org

A commutative integral domain with unique factorization of ideals is called a Dedekind domain; such a ring is necessarily Noetherian, i.e., it satisfies the as-.

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