2021
DOI: 10.48550/arxiv.2101.05441
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Length-factoriality in commutative monoids and integral domains

Abstract: An atomic monoid M is called a length-factorial monoid (or an other-half-factorial monoid) if for each non-invertible element x ∈ M no two distinct factorizations of x have the same length. The notion of length-factoriality was introduced by Coykendall and Smith in 2011 as a dual of the well-studied notion of half-factoriality. They proved that in the setting of integral domains, lengthfactoriality can be taken as an alternative definition of a unique factorization domain. However, being a length-factorial mon… Show more

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