# A potpourri of algebraic properties of the ring of periodic distributions

## TL;DR

This paper explores various algebraic properties of the ring of periodic distributions, highlighting its structure and isomorphism to sequence rings of polynomial growth, enriching the understanding of their algebraic behavior.

## Contribution

The paper systematically investigates algebraic properties of the ring of periodic distributions and establishes its isomorphism to sequence rings of polynomial growth.

## Key findings

- The ring of periodic distributions has specific algebraic properties.
- It is isomorphic to the ring of sequences with polynomial growth.
- Several algebraic properties of these rings are established.

## Abstract

The set of periodic distributions, with usual addition and convolution, forms a ring, which is isomorphic, via taking a Fourier series expansion, to the ring ${\mathcal{S}}'({\mathbb{Z}}^d)$ of sequences of at most polynomial growth with termwise operations. In this article, we establish several algebraic properties of these rings.