Central orders in simple right-alternative superalgebras and right-symmetric algebras

TL;DR

This paper investigates the structure of simple finite-dimensional right-alternative superalgebras and right-symmetric algebras, showing their central orders embed into finite modules over their centers, advancing understanding of their algebraic properties.

Contribution

It proves that the central order of these algebras embeds into a finite module over its center, providing new structural insights.

Findings

Central orders embed into finite modules over their centers

Results apply to recently constructed simple superalgebras

Enhances understanding of algebraic structure in superalgebras

Abstract

We consider some recently constructed examples of simple finite-dimensional right-alternative superalgebras and right-symmetric algebras. We prove that the central order in any of these algebras and superalgebras is embedded in a finite module over its center (or over the even part of its center in the case of superalgebras)