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arXiv · 1309.7477

Factorization Properties of Leamer Monoids

Jason Haarmann·Ashlee Kalauli·Aleesha Moran·Christopher O'Neill·Roberto Pelayo
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Abstract

The Huneke-Wiegand conjecture has prompted much recent research in Commutative Algebra. In studying this conjecture for certain classes of rings, García-Sánchez and Leamer construct a monoid S_Γ^s whose elements correspond to arithmetic sequences in a numerical monoid Γof step size s. These monoids, which we call Leamer monoids, possess a very interesting factorization theory that is significantly different from the numerical monoids from which they are derived. In this paper, we offer much of the foundational theory of Leamer monoids, including an analysis of their atomic structure, and investigate certain factorization invariants. Furthermore, when S_Γ^s is an arithmetical Leamer monoid, we give an exact description of its atoms and use this to provide explicit formulae for its Delta set and catenary degree.

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Jason Haarmann, Ashlee Kalauli, Aleesha Moran, Christopher O'Neill, Roberto Pelayo. 2014-05-07. Factorization Properties of Leamer Monoids. https://doi.org/10.1007/s00233-014-9578-z

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