Some properties of (C,E,P)-algebras : Overgneration and 0-order estimates

TL;DR

This paper introduces a new definition of overgenerated rings within (C,E,P)-algebras and demonstrates that moderate elements are negligible if they meet specific order estimates, refining the understanding of their asymptotic structure.

Contribution

It provides a novel definition of overgenerated rings and establishes a characterization of negligible elements via C*-order estimates in (C,E,P)-algebras.

Findings

New definition of overgenerated rings for (C,E,P)-algebras

Characterization of negligible elements using C*-order estimates

Enhanced understanding of the asymptotic structure of (C,E,P)-algebras

Abstract

We give a new definition of the so-called overgenerated rings, which are the usual tool used to define the asymptotic structure of a (C,E,P)-algebra, written as a factor space M_{(A,E,P)}/N_{(I_{A},E,P)}. With this new definition and in the particular case of E=C^{∞}, we show that a moderate element i.e. in M_{(A,E,P)} is negligible if and only if it satisfies the C⁰-order estimate for the ideal N_{(I_{A},E,P)}.