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".
- ASN: Alec's Standard Notation