pring
Definition 1.
Let $R$ be a commutative ring with identity element^{} equipped with a topology defined by a decreasing sequence:
$$\mathrm{\dots}\subset {\U0001d504}_{3}\subset {\U0001d504}_{2}\subset {\U0001d504}_{1}$$ 
of ideals such that ${\mathrm{A}}_{n}\mathrm{\cdot}{\mathrm{A}}_{m}\mathrm{\subset}{\mathrm{A}}_{n\mathrm{+}m}$. We say that $R$ is a $p$ring if the following conditions are satisfied:

1.
The residue ring $\overline{k}=R/{\U0001d504}_{1}$ is a perfect ring of characteristic^{} $p$.

2.
The ring $R$ is Hausdorff and complete^{} for its topology.
Definition 2.
A $p$ring $R$ is said to be strict (or a $p$adic ring) if the topology is defined by the $p$adic filtration^{} ${\mathrm{A}}_{n}\mathrm{=}{p}^{n}\mathit{}R$, and $p$ is not a zerodivisor of $R$.
Example 1.
The prototype of strict $p$ring is the ring of $p$adic integers (http://planetmath.org/PAdicIntegers) ${\mathbb{Z}}_{p}$ with the usual profinite topology.
References
 1 J. P. Serre, Local Fields^{}, SpringerVerlag, New York.
Title  pring 

Canonical name  Pring 
Date of creation  20130322 15:14:28 
Last modified on  20130322 15:14:28 
Owner  alozano (2414) 
Last modified by  alozano (2414) 
Numerical id  4 
Author  alozano (2414) 
Entry type  Definition 
Classification  msc 13J10 
Classification  msc 13K05 
Synonym  $p$ring 
Synonym  padic ring 
Synonym  $p$adic ring 
Synonym  strict $p$ring 
Defines  strict pring 