For which additive submonoids $M$ of nonnegative rationals is $F[X;M]$ AP?

Ryan Gipson; Hamid Kulosman

For which additive submonoids $M$ of nonnegative rationals is $F[X;M]$ AP?

Commutative Algebra 2018-05-29 v1

Authors: Ryan Gipson , Hamid Kulosman

Abstract

We characterize the submonoids $M$ of the additive monoid $\Q_+$ of nonnegative rational numbers for which the irreducible and the prime elements in the monoid domain $F[X;M]$ coincide. We present a diagram of implications between some types of submonoids of $\Q_+$ , with a precise position of the monoids $M$ with this property.

Keywords

additive submonoids nonnegative rationals monoid domain irreducible elements prime elements AP domains

Cite

@article{arxiv.1805.10373,
  title  = {For which additive submonoids $M$ of nonnegative rationals is $F[X;M]$ AP?},
  author = {Ryan Gipson and Hamid Kulosman},
  journal= {arXiv preprint arXiv:1805.10373},
  year   = {2018}
}

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