# On Quasi-Symmetric Polynomially Bounded Fr\'echet Algebras

## TL;DR

This paper explores the structure of quasi-symmetric polynomially bounded Fréchet algebras, focusing on their symmetry properties, hull-kernel regularity, and the existence of hull-minimal ideals.

## Contribution

It introduces and analyzes the concept of quasi-symmetric algebras, extending the theory of symmetric algebras within the context of Fréchet algebras.

## Key findings

- Characterization of hull-kernel regularity in quasi-symmetric algebras
- Existence criteria for hull-minimal ideals in these algebras
- Structural insights into the generalization from symmetric to quasi-symmetric algebras

## Abstract

This paper concerns the notion of a symmetric algebra and its generalization to a quasi-symmetric algebra. We study the structure of these algebras in respect to their hull-kernel regularity and existence of some ideals, especially the hull-minimal ideals.