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 \(\mathrm{Cl}(A)\) of A and the class group \(\mathrm{Cl}(B)\) of B. In this direction, we give a sufficient condition for an injective group homomorphism from \(\mathrm{Cl}(A)\) to \(\mathrm{Cl}(B)\). We also give an example to show that \(\mathrm{Cl}(A)\) may not be realized as a subgroup of \(\mathrm{Cl}(B)\).
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Acknowledgements
This work was done while the first author was holding INSA Senior Scientist position. He wishes to express his gratitude to the Indian National Science Academy (INSA) for financial support.
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Communicating Editor: Mrinal Kanti Das
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Bhatwadekar, S.M., Majithia, J.T. Class group of the ring of invariants of an exponential map on an affine normal domain. Proc Math Sci 130, 3 (2020). https://doi.org/10.1007/s12044-019-0536-2
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DOI: https://doi.org/10.1007/s12044-019-0536-2