On the atomic structure of torsion-free monoids
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Author(s)
Gotti, Felix
Vulakh, Joseph
Date Issued
October 3, 2023
Publisher
Springer US
Citation
Gotti, Felix and Vulakh, Joseph. 2023. "On the atomic structure of torsion-free monoids."
Version
Final published version
Abstract
Abstract
Let M be a cancellative and commutative (additive) monoid. The monoid M is atomic if every non-invertible element can be written as a sum of irreducible elements, which are also called atoms. Also, M satisfies the ascending chain condition on principal ideals (ACCP) if every increasing sequence of principal ideals (under inclusion) becomes constant from one point on. In the first part of this paper, we characterize torsion-free monoids that satisfy the ACCP as those torsion-free monoids whose submonoids are all atomic. A submonoid of the nonnegative cone of a totally ordered abelian group is often called a positive monoid. Every positive monoid is clearly torsion-free. In the second part of this paper, we study the atomic structure of certain classes of positive monoids.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
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DOI of Published Version
https://doi.org/10.1007/s00233-023-10385-8
