Class group of the ring of invariants of an exponential map on an affine normal domain
Click here to view fulltext PDF
Permanent link:
https://www.ias.ac.in/article/fulltext/pmsc/130/0003
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)$.
S M BHATWADEKAR1 J T MAJITHIA2
Volume 130, 2020
All articles
Continuous Article Publishing mode
Click here for Editorial Note on CAP Mode
© 2021-2022 Indian Academy of Sciences, Bengaluru.