On the PI-exponent of matrix algebras and algebras with generalized actions
Fuente:
arXiv
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866909660668231680 |
|---|---|
| author | de Mello, Thiago Castilho Yasumura, Felipe Yukihide |
| author_facet | de Mello, Thiago Castilho Yasumura, Felipe Yukihide |
| contents | We compute the PI-exponent of the matrix ring with coefficients in an associative algebra. As a consequence, we prove the following. Let $\mathcal{R}$ be a PI-algebra with a positive PI-exponent. If $M_n(\mathcal{R})$ and $M_m(\mathcal{R})$ satisfy the same set of polynomial identities then $n=m$. We provide examples where this result fails if either $\mathcal{R}$ is not PI or has zero exponent. We obtain the same statement for certain finite-dimensional algebras with generalized action over an algebraically closed field of zero characteristic. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_21257 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On the PI-exponent of matrix algebras and algebras with generalized actions de Mello, Thiago Castilho Yasumura, Felipe Yukihide Rings and Algebras We compute the PI-exponent of the matrix ring with coefficients in an associative algebra. As a consequence, we prove the following. Let $\mathcal{R}$ be a PI-algebra with a positive PI-exponent. If $M_n(\mathcal{R})$ and $M_m(\mathcal{R})$ satisfy the same set of polynomial identities then $n=m$. We provide examples where this result fails if either $\mathcal{R}$ is not PI or has zero exponent. We obtain the same statement for certain finite-dimensional algebras with generalized action over an algebraically closed field of zero characteristic. |
| title | On the PI-exponent of matrix algebras and algebras with generalized actions |
| topic | Rings and Algebras |
| url | https://arxiv.org/abs/2506.21257 |