Difference between revisions of "U-ring"
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==Definition== | ==Definition== | ||
| − | A ''u-ring'' (say: "''you-ring''") is a term for a [[ | + | 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|Motivation]]== | ==[[/Motivation|Motivation]]== | ||
{{/Motivation}} | {{/Motivation}} | ||
==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. | ||
| + | |||
==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
Contents
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".
