• Class group of the ring of invariants of an exponential map on an affine normal domain

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    • 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

      1. Bhaskaracharya Pratishthana, 56/14 Erandavane, Damle Path, Off Law College Road, Pune 411 004, India
      2. Department of Mathematics, College of Engineering Pune, Shivajinagar, Pune 411 005, India
    • Dates

       
  • Proceedings – Mathematical Sciences | News

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