English

On properties of square-free elements in commutative cancellative monoids

Commutative Algebra 2019-01-01 v1

Abstract

We discuss various square-free factorizations in monoids in the context of: atomicity, ascending chain condition for principal ideals, decomposition, and a greatest common divisor property. Moreover, we obtain a full characterization of submonoids of factorial monoids in which all square-free elements of a submonoid are square-free in a monoid. We also present factorial properties implying that all atoms of a submonoid are square-free in a monoid.

Keywords

Cite

@article{arxiv.1812.11882,
  title  = {On properties of square-free elements in commutative cancellative monoids},
  author = {Piotr Jędrzejewicz and Mikołaj Marciniak and Łukasz Matysiak and Janusz Zieliński},
  journal= {arXiv preprint arXiv:1812.11882},
  year   = {2019}
}

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23 pages