Journal of Commutative Algebra

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 $B[N]$ 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).

Article information

Source
J. Commut. Algebra, Volume 9, Number 2 (2017), 303-312.

Dates
First available in Project Euclid: 3 June 2017

Permanent link to this document
https://projecteuclid.org/euclid.jca/1496476826

Digital Object Identifier
doi:10.1216/JCA-2017-9-2-303

Mathematical Reviews number (MathSciNet)
MR3659953

Zentralblatt MATH identifier
1372.13002

Subjects
Primary: 13A15: Ideals; multiplicative ideal theory 13B99: None of the above, but in this section 13C10: Projective and free modules and ideals [See also 19A13]

Keywords
Invertible modules monoid extensions monoid algebras

Citation

Sarwar, Husney Parvez. Ideal class groups of monoid algebras. J. Commut. Algebra 9 (2017), no. 2, 303--312. doi:10.1216/JCA-2017-9-2-303. https://projecteuclid.org/euclid.jca/1496476826


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