Principal ideal：Principal ideal

Principal ideal

Inmathematics,specificallyringtheory,aprincipalidealisanidealI-displaystyleI}IinaringR-displaystyleR}Rthatisgeneratedbyasingle ...。其他文章還包含有：「PrincipalIdeal」、「代數導論二Week3(Part4)」、「Principalidealdomain」、「Principalidealring」、「主要理想PrincipalIdeal」、「Principalidealtheorem」、「PrincipleIdealDomain」、「AbstractAlgebra」

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RingidealgeneratedbyasingleelementoftheringInmathematics,specificallyringtheory,aprincipalidealisanidealI{\displaystyleI}inaringR{\displaystyleR}thatisgeneratedbyasingleelementa{\displaystylea}ofR{\displaystyleR}throughmultiplicationbyeveryelementofR.{\displaystyleR.}Thetermalsohasanother,similarmeaninginordertheory,whereitreferstoan(order)idealinaposetP{\displaystyleP}generatedbyasingleelementx∈P,{\displaystylex\inP,}whichistosaythesetofallelementslessthanorequaltox{\displaystylex}inP.{\dis...

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Principal Ideal

https://mathworld.wolfram.com

An ideal I of a ring R is called principal if there is an element a of R such that I=aR=ar:r in R}. In other words, the ideal is generated by the element a ...

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代數導論二Week 3 (Part 4)

https://hackmd.io

定義：Principal Ideal Domain. Suppose R R is an integral domain. If every ideal in R R is a principal ideal, them R R is said to be a Princpal Ideal Domain.

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Principal ideal domain

https://en.wikipedia.org

In mathematics, 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.

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Principal ideal ring

https://en.wikipedia.org

In mathematics, a principal right (left) ideal ring is a ring R in which every right (left) ideal is of the form xR (Rx) for some element x of R. (The right ...

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主要理想Principal Ideal

https://academic-accelerator.c

所有理想均為主理想的環稱為主理想環或主理想環。主理想域(PID) 是所有理想占主導地位的積分域。每個PID 都是一個唯一的分解域。整數唯一分解的通常證明（所謂的算術基本 ...

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Principal ideal theorem

https://en.wikipedia.org

In mathematics, the principal ideal theorem of class field theory, a branch of algebraic number theory, says that extending ideals gives a mapping on the ...

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