2018/12/31 by Piotr Jędrzejewicz, Mikołaj Marciniak, Jędrzejewicz, Piotr +6
Computer Science · Mathematics · #Advanced Algebra and Logic #Rings, Modules, and Algebras #math.AC #msc:13F15 #msc:20M14 #semigroups and automata theory
paper · pdf · doi:10.48550/arxiv.1812.11882
23 pages
arxiv created 2018/12/31 · arxiv updated 2019/01/01
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.