Ideal class groups of monoid algebras

2014/09/01 by Husney Parvez Sarwar, Sarwar, Husney Parvez · 1 citation
Mathematics · #13B99 #Commutative Algebra (math.AC) #FOS: Mathematics #math.AC #msc:13B99

paper · pdf · doi:10.48550/arxiv.1409.0299

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

arxiv created 2015/05/20 · arxiv updated 2015/05/21

Abstract

Let A⊂ B be an extension of commutative reduced rings and M⊂ 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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• Subintegrality and ideal class groups of monoid algebras

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