Rigidity and triangularity of an exponential map
Fuente:
arXiv
Salvato in:
| Autore principale: | |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2023
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866910748211412992 |
|---|---|
| author | Krishna, P. M. S. Sai |
| author_facet | Krishna, P. M. S. Sai |
| contents | Let $k$ be a field of arbitrary characteristic, $A$ be a domain and $K=\mathrm{frac}(A)$. Then
(1) All exponential maps of $k^{[3]}$ are rigid, and we give a necessary and sufficient condition for the triangularity of $δ\in \mathrm{EXP}(k^{[3]})$.
(2) If $δ\in \mathrm{EXP}(A^{[3]})$ such that $\mathrm{rank}(δ)=\mathrm{rank}(δ_K)$, then $δ$ is rigid and we give a necessary and sufficient condition for the triangularity of $δ$.
When $k$ is of zero characteristic, $(1)$ is due to \cite{DD} and $(2)$ is due to \cite{KL}. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2312_01750 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Rigidity and triangularity of an exponential map Krishna, P. M. S. Sai Commutative Algebra Let $k$ be a field of arbitrary characteristic, $A$ be a domain and $K=\mathrm{frac}(A)$. Then (1) All exponential maps of $k^{[3]}$ are rigid, and we give a necessary and sufficient condition for the triangularity of $δ\in \mathrm{EXP}(k^{[3]})$. (2) If $δ\in \mathrm{EXP}(A^{[3]})$ such that $\mathrm{rank}(δ)=\mathrm{rank}(δ_K)$, then $δ$ is rigid and we give a necessary and sufficient condition for the triangularity of $δ$. When $k$ is of zero characteristic, $(1)$ is due to \cite{DD} and $(2)$ is due to \cite{KL}. |
| title | Rigidity and triangularity of an exponential map |
| topic | Commutative Algebra |
| url | https://arxiv.org/abs/2312.01750 |