Articles written in Proceedings – Mathematical Sciences

• Generalized epimorphism theorem

LetR[X, Y] be a polynomial ring in two variables over a commutative ringR and letF∈R[X, Y] such thatR[X, Y]/(F)=R[Z] (a polynomial ring in one variable). In this set-up we prove thatR[X, Y]=R[F, G] for someG∈R[X, Y] if eitherR contains a field of characteristic zero orR is a seminormal domain of characteristic zero.

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

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)$.

• # Proceedings – Mathematical Sciences

Volume 131, 2021
All articles
Continuous Article Publishing mode

• # Editorial Note on Continuous Article Publication

Posted on July 25, 2019