Saved in:
| Main Authors: | , , , |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2401.12897 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866914649527549952 |
|---|---|
| author | Calderón, Antonio J. Díaz, Antonio Haralampidou, Marina Sánchez, José M. |
| author_facet | Calderón, Antonio J. Díaz, Antonio Haralampidou, Marina Sánchez, José M. |
| contents | Consider a pseudo-$H$-space $E$ endowed with a separately continuous biadditive associative multiplication which induces a grading on $E$ with respect to an abelian group $G$. We call such a space a graded pseudo-$H$-ring and we show that it has the form $E = cl(U + \sum_j I_j)$ with $U$ a closed subspace of $E_1$ (the summand associated to the unit element in $G$), and any $I_j$ runs over a well described closed graded ideal of $E$, satisfying $I_jI_k = 0$ if $j \neq k$. We also give a context in which graded simplicity of $E$ is characterized. Moreover, the second Wedderburn-type theorem is given for certain graded pseudo-$H$-rings. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_12897 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Graded pseudo-H-rings Calderón, Antonio J. Díaz, Antonio Haralampidou, Marina Sánchez, José M. Rings and Algebras Consider a pseudo-$H$-space $E$ endowed with a separately continuous biadditive associative multiplication which induces a grading on $E$ with respect to an abelian group $G$. We call such a space a graded pseudo-$H$-ring and we show that it has the form $E = cl(U + \sum_j I_j)$ with $U$ a closed subspace of $E_1$ (the summand associated to the unit element in $G$), and any $I_j$ runs over a well described closed graded ideal of $E$, satisfying $I_jI_k = 0$ if $j \neq k$. We also give a context in which graded simplicity of $E$ is characterized. Moreover, the second Wedderburn-type theorem is given for certain graded pseudo-$H$-rings. |
| title | Graded pseudo-H-rings |
| topic | Rings and Algebras |
| url | https://arxiv.org/abs/2401.12897 |