Difference between revisions of "U-ring"

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==Definition==
 
==Definition==
A ''u-ring'' (say: "''you-ring''") is a term for a [[ring|ring with unity]]<sup>[[ASN]]:</sup><ref>[[ASN]]: Alec's Standard Notation</ref>.
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A ''u-ring'' (say: "''you-ring''") is a term for a [[ring with unity]]<sup>[[ASN]]:</sup><ref>[[ASN]]: Alec's Standard Notation</ref>.
==Motivation==
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==[[/Motivation|Motivation]]==
Some authors (a considerable number) consider a ring to be what we would call a ring-with-unity, this is because almost all the rings they cover have unity, so it makes sense, "Let {{M|R}} be a ring" is shorter than "Let {{M|R}} be a ring with unity" over and over again.
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{{/Motivation}}
 
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To get the best of both, I decided to use "u-ring", "c-ring" (for a commutative ring) and "cu-ring" for a "commutative ring with unity", which only adds 2 or 3 more characters to "ring".
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A ''cu-ring'' can be said "see-you-ring" or "cue-ring" (phonetically: "queue-ring"), this may be written "q-ring"
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As always, letters like this will be alphabetical, it isn't "uc-ring".
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==See also==
 
==See also==
 +
* [[c-ring]] - a commutative ring.
 
* [[cu-ring]] ({{AKA}}: [[q-ring]]) - a ''[[commutative]]'' [[ring]] with unity.
 
* [[cu-ring]] ({{AKA}}: [[q-ring]]) - a ''[[commutative]]'' [[ring]] with unity.
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==References==
 
==References==
 
<references/>
 
<references/>
 
{{Definition|Abstract Algebra|Ring Theory}}[[Category:ASN]]
 
{{Definition|Abstract Algebra|Ring Theory}}[[Category:ASN]]

Latest revision as of 16:32, 19 October 2016

Definition

A u-ring (say: "you-ring") is a term for a ring with unityASN:[1].

Motivation

Some authors (a considerable number) consider a ring to be what we would call a ring-with-unity, this is because almost all the rings they cover have unity, so it makes sense, "Let [ilmath]R[/ilmath] be a ring" is shorter than "Let [ilmath]R[/ilmath] be a ring with unity" over and over again.

To get the best of both, I decided to use "u-ring", "c-ring" (for a commutative ring) and "cu-ring" for a "commutative ring with unity", which only adds 2 or 3 more characters to "ring".

A cu-ring can be said "see-you-ring" or "cue-ring" (phonetically: "queue-ring"), this may be written "q-ring"

As always, letters like this will be alphabetical, it isn't "uc-ring".

See also

References

  1. ASN: Alec's Standard Notation