A linear algebra characterization of the semisimplicity and the simplicity of arbitrary algebras
Fuente:
arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866916420919492608 |
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| author | Martin, Antonio J. Calderon |
| author_facet | Martin, Antonio J. Calderon |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_01938 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A linear algebra characterization of the semisimplicity and the simplicity of arbitrary algebras Martin, Antonio J. Calderon Rings and Algebras 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. |
| title | A linear algebra characterization of the semisimplicity and the simplicity of arbitrary algebras |
| topic | Rings and Algebras |
| url | https://arxiv.org/abs/2410.01938 |