Abstract
Let \(\Gamma \) be a numerical semigroup. The Leamer monoid \(S_\Gamma ^s\), for \(s\in \mathbb {N}\backslash \Gamma \), is the monoid consisting of arithmetic sequences of step size s contained in \(\Gamma \). In this note, we give a formula for the \(\omega \)-primality of elements in \(S_\Gamma ^s\) when \(\Gamma \) is an numerical semigroup generated by a arithmetic sequence of positive integers.
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It is a pleasure for the authors to thank an unknown referee for comments that greatly improved the final manuscript.
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Communicated by Fernando Torres.
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Both author gratefully acknowledge support from the National Science Foundation under Grant DMS-1262897. The first author also acknowledges support under an Academic Leave funded by Sam Houston State University.
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Chapman, S.T., Tripp, Z. \(\omega \)-Primality in arithmetic Leamer monoids. Semigroup Forum 99, 47–56 (2019). https://doi.org/10.1007/s00233-019-10036-x
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DOI: https://doi.org/10.1007/s00233-019-10036-x