Ideal class groups of monoid algebras

Husney Parvez Sarwar

Ideal class groups of monoid algebras

Commutative Algebra 2015-05-21 v2

Authors: Husney Parvez Sarwar

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.

Keywords

monoids module theory commutative ring theory

Cite

@article{arxiv.1409.0299,
  title  = {Ideal class groups of monoid algebras},
  author = {Husney Parvez Sarwar},
  journal= {arXiv preprint arXiv:1409.0299},
  year   = {2015}
}

Comments

Title is changed. Main theorem is improved significantly, viz, relative version of monoid is considered. Final version is going to appear in Journal of Commutative Algebra

Ideal class groups of monoid algebras

Abstract

Keywords

Cite

Comments

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