Definition talk:P-adic Integer

$p$-adic Integers Notation

A decision needs to be made regarding the notation to be used for the $p$-adic integers.

In many sources the notation $\Z_p$ is used to denote the $p$-adic integers but this notation is used on $\mathsf{Pr} \infty \mathsf{fWiki}$ for the ring of integers module $p$ where $p$ is a prime number.

So I’m looking for some thoughts and direction for the notation to be used on $\mathsf{Pr} \infty \mathsf{fWiki}$ for the $p$-adic integers. I’ve tentatively suggested $\mathbf {Z}_p$, but I’m in no way wedded to this as this could still be seen as conflicting with ring of integers module $p$.

Other possibilities could be $\mathbb {I}_p$ or $\mathbb {J}_p$ since $\mathbb {I}$ and $\mathbb {J}$ are sometimes used for the integers, but I haven’t seen either of these used anywhere. I’ve only seen $\Z_p$ or $\mathbf {Z}_p$ used for the $p$-adic integers in the 4 books I have and in online sources.

—Leigh.Samphier (talk) 06:57, 8 March 2019 (EST)

How vitally important is it that it has to be unique? --prime mover (talk) 12:41, 8 March 2019 (EST)

So long as all occurrences of $\Z_p$ suitably define what is referred to then there is no issue. I found 10 instances on $\mathsf{Pr} \infty \mathsf{fWiki}$ where $\Z_p$ was used without defining what $\Z_p$ was. These could be changed to explicitly define $\Z_p$. There are many instances of $\Z_m$ where this is not defined, but $m$ is any positive integer and so can't refer to the $p$-adic integers. So I could use $\Z_p$ if I clarify existing uses, in keeping with most sources. --Leigh.Samphier (talk) 22:37, 8 March 2019 (EST)

Where are those places? Every place where a symbol is user, it is mandatory that it be defined. Tell me where those places are, and the authors will be banned from further contribution to this site. --prime mover (talk) 02:47, 9 March 2019 (EST)

I'll leave that one alone. I'll use $\Z_p$ and make sure that from the context that the definition of $\Z_p$ is clear for anything that I work on. --Leigh.Samphier (talk) 01:36, 10 March 2019 (EST)