Open Access
2017 Ideal class groups of monoid algebras
Husney Parvez Sarwar
J. Commut. Algebra 9(2): 303-312 (2017). DOI: 10.1216/JCA-2017-9-2-303


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 $B[N]$ Theorem~\ref {6t2} (b), (d). In the case $M=N$, we prove the same without the assumption that the ring extension is reduced Theorem~\ref {6t2} (c), (d).


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Husney Parvez Sarwar. "Ideal class groups of monoid algebras." J. Commut. Algebra 9 (2) 303 - 312, 2017.


Published: 2017
First available in Project Euclid: 3 June 2017

zbMATH: 1372.13002
MathSciNet: MR3659953
Digital Object Identifier: 10.1216/JCA-2017-9-2-303

Primary: 13A15 , 13B99 , 13C10

Keywords: Invertible modules , monoid algebras , monoid extensions

Rights: Copyright © 2017 Rocky Mountain Mathematics Consortium

Vol.9 • No. 2 • 2017
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