Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Ideal class groups of monoid algebras   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.

35
The categories of this paper are: mtrl-th
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The categories of this paper are: supr-con
13
The categories of this paper are: quant-ph
16
The categories of this paper are: stat
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The categories of this paper are: funct-an
30
The categories of this paper are: q-alg
18
The categories of this paper are: econ
26
The categories of this paper are: bayes-an
25
The categories of this paper are: patt-sol
5
The categories of this paper are: gr-qc
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The categories of this paper are: chem-ph
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The categories of this paper are: alg-geom
4
The categories of this paper are: cond-mat
10
The categories of this paper are: q-bio
22
The categories of this paper are: chao-dyn
12
The categories of this paper are: nucl-th