-
- Home
- Journals
- Proceedings – Mathematical Sciences
- Volume 130
- All articles
-
Class group of the ring of invariants of an exponential map on an affine normal domain
Research Article Volume 130 Published: 10 January 2020 Article ID 0003
-
-
Fulltext
Click here to view fulltext PDF
Permanent link:
https://www.ias.ac.in/article/fulltext/pmsc/130/0003 -
Keywords
Exponential map ;ring of invariants ;Krull domain ;class group ;Rees algebra -
Abstract
Let $k$ be a field and let $B$ be an affine normal domain over $k$. Let $\phi$ be a non-trivial exponential map on $B$ and let $A = B^{\phi}$ be the ring of $\phi$-invariants. Since $A$ is factorially closed in $B$, $A = K \cap B$ where $K$ denotes the field of fractions of $A$. Hence $A$ is a Krull domain. We investigate here a relation between the class group $\rm{Cl}$$(A)$ of $A$ and the class group $\rm{Cl}$$(B)$ of $B$. In this direction, we give a sufficient condition for an injective group homomorphism from $\rm{Cl}$$(A)$ to $\rm{Cl}$$(B)$. We also give an example to show that $\rm{Cl}$$(A)$ may not be realized as a subgroup of $\rm{Cl}$$(B)$.
-
Author Affiliations
S M BHATWADEKAR1 J T MAJITHIA2
- Bhaskaracharya Pratishthana, 56/14 Erandavane, Damle Path, Off Law College Road, Pune 411 004, India
- Department of Mathematics, College of Engineering Pune, Shivajinagar, Pune 411 005, India
-
Dates
- Published
- 10 January 2020
- Manuscript received
- 19 April 2019
- Manuscript revised
- 14 May 2019
- Accepted
- 21 May 2019
- Early published
- Unedited version published online
- Final version published online
- 3 January 2020
-
-
Proceedings – Mathematical Sciences
Volume 131, 2021
All articles
Continuous Article Publishing mode
-
Proceedings – Mathematical Sciences | News
-
Editorial Note on Continuous Article Publication
Posted on July 25, 2019Click here for Editorial Note on CAP Mode
-