2000 character limit reached
A linear algebra characterization of the semisimplicity and the simplicity of arbitrary algebras (2410.01938v1)
Published 2 Oct 2024 in math.RA
Abstract: We show that an arbitrary algebra ${ A}$, (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 $A$ is simple if and only if it has zero annihilator and admits an $i$-division linear basis.