Derivation on Vinberg rings

Gangireddy Lakshmi Devi,Karamsi Jayalakshmi

doi:10.5269/bspm.v37i3.31684

Abstract

A nonassociative ring which contains a well-known associative ring or left symmetric ring also known as Vinberg ring is of great interest. A method to construct Vinberg nonassociative ring is given; Vinberg nonassociative ring is shown as simple; all the derivations of nonassociative simple Vinberg algebra defined are determined; and finally in solid algebra it is shown that if is a nonzero endomorphism of , then is an epimorphism.

Highlights

With the obvious addition and the multiplication [3, 4, 6, 7]
We prove that the ring V Nn,m,s is simple
We have proved that ∂w = V Nn,m,s

Summary

Introduction

With the obvious addition and the multiplication [3, 4, 6, 7]. We define the F Vector space V N(n,m,s) with the standard basis. We can define the Vinberg-type nonassociative ring V Nn,m,s with the multiplication in (1.4) and with the set V N(n,m,s). Let I be a non - zero ideal of V Nn,m,s. Let us prove the theorem by induction on the number of distinct homogeneous components of any non - zero element l in I.

Results

Conclusion