A linear algebra characterization of the semisimplicity and the simplicity of arbitrary algebras
Rings and Algebras
2024-10-04 v1
Abstract
We show that an arbitrary algebra , (of arbitrary dimension, over an arbitrary base field and any identity is not suppose for the product), is semisimple if and only if it has zero annihilator and admits a semi-division linear basis. We also show that is simple if and only if it has zero annihilator and admits an -division linear basis.
Cite
@article{arxiv.2410.01938,
title = {A linear algebra characterization of the semisimplicity and the simplicity of arbitrary algebras},
author = {Antonio J. Calderon Martin},
journal= {arXiv preprint arXiv:2410.01938},
year = {2024}
}