Local Systems of Simple Locally Finite Associative Algebras

TL;DR

This paper investigates local systems of locally finite associative algebras over fields of any characteristic, describing perfect systems and their relations, with brief considerations of conical systems.

Contribution

It introduces a detailed analysis of perfect local systems and their connection to locally finite associative algebras, including new classifications like conical systems.

Findings

Characterization of perfect local systems

Relationship between local systems and associative algebras

Brief description of conical local systems

Abstract

In this paper, we study local systems of locally finite associative algebras over fields of characteristic p\ge0. We describe the perfect local systems and study the relation between them and their corresponding locally finite associative algebras. 1-perfect and conical local systems are also be considered and described briefly.