Math @ Duke

Publications [#219347] of Christopher O'Neill
Papers Submitted
 J. Haarmann, A. Kalauli, A. Moran, C. O'Neill, R. Pelayo, Factorization Properties of Leamer Monoids,
Semigroup Forum
(2013) [arXiv:1309.7477]
(last updated on 2013/11/03)
Abstract: The HunekeWiegand conjecture has prompted much recent research in Commutative Algebra. In studying this conjecture for certain classes of rings, GarciaSanchez and Leamer construct a monoid S_Gamma^s whose elements correspond to arithmetic sequences in a numerical monoid Gamma of 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_Gamma^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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