Principal ideal

Aringinwhicheveryidealisprincipaliscalledprincipal,oraprincipalidealring.Aprincipalidealdomain(PID)isanintegraldomaininwhichevery ...。其他文章還包含有：「Principalidealring」、「PrincipalRing」、「PrincipleRing|Silver」、「Principalidealdomain」、「PrincipalIdeal」、「中級Ring的性質」、「Principalidealring」

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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 ring

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A local Artinian principal ring is called a special principal ring and has an extremely simple ideal structure: there are only finitely many ideals, each of ...

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Principal Ring

https://mathworld.wolfram.com

Principal Ring ... , any field, and any polynomial ring in one variable over a field. While all Euclidean rings are principal rings, the converse is not true.

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Principle Ring|Silver

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Principle Ring|Silver · 925 sterling silver · SIZE：1.7 cm (diameter)/ 1.4 cm (thick) (Slightly adjustable ring size) · One Piece.

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Principal ideal domain

https://en.wikipedia.org

More generally, a principal ideal ring is a nonzero commutative ring whose ideals are principal, although some authors (e.g., Bourbaki) refer to PIDs as ...

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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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