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arXiv · 1409.0299

Ideal class groups of monoid algebras

Husney Parvez Sarwar
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Abstract

Let $A\subset B$ be an extension of commutative reduced rings and $M\subset N$ an extension of positive commutative cancellative torsion-free monoids. We prove that $A$ is subintegrally closed in $B$ and $M$ is subintegrally closed in $N$ if and only if the group of invertible $A$-submodules of $B$ is isomorphic to the group of invertible $A[M]$-submodules of $B[N]$. In case $M=N$, we prove the same without the assumption that the ring extension is reduced.

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Husney Parvez Sarwar. 2014-09-01. Ideal class groups of monoid algebras. https://arxiv.org/abs/1409.0299

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