There was a discussion at GitHub (issue #866 
<https://github.com/metamath/set.mm/issues/866>) with the following result:

Definition: df-zzring $a |- ZZring = ( CCfld |``s ZZ )
Symbol: ℤring (althtmldef "ZZring" as "&#8484;<SUB>ring</SUB>"; ):

These will be availble in set.mm soon.


On Thursday, May 30, 2019 at 8:25:58 AM UTC+2, Alexander van der Vekens 
wrote:
>
> Recently I moved the section "The ordered commutative ring of integers" in 
> TA's mathbox into the main part, as section "10.11.2 Ring of integers", see 
> http://us2.metamath.org:88/mpeuni/mmtheorems176.html and also Issue #866 
> <https://github.com/metamath/set.mm/issues/866> at GitHub. There is, 
> however, not a definition of the ring of integers yet, but it is 
> represented as restriction of the field of complex numbers ( CCfld |`s ZZ ) 
> . Since, in my opinion, the "Ring of integers" is an important and central 
> concept in mathematics, I think it deserves a particular definition.
>
>
> My suggestion would be
>
> df-rngz $a |- RingZ = ( CCfld |`s ZZ ) . 
>
>
> As symbol to be used in HTML we could use ℤrng (analogously to ℂfld for 
> CCfld).
>
>
> Unfortunately, there is already a definition df-zrng $a |- ZRing = ... in 
> Mario's Mathbox (subring of integral elements in a ring), so ZRing cannot 
> be used for the "Ring of integers" (or Mario's definition must be changed). 
> Alternatively, we could use ZZRing or ZZRng or ZZrng (this is closest to 
> CCfld) for the "Ring of integers".
>
>
> What do you think about this? Which (of the proposed) class name(s) do you 
> prefer?
>

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