Publications of Christopher O'Neill    :chronological  alphabetical  combined listing:

%% Papers Accepted   
@article{fds221103,
   Author = {C. O'Neill and R. Pelayo},
   Title = {On the Linearity of Omega-Primality in Numerical
             Monoids},
   Journal = {Journal of Pure and Applied Algebra},
   Year = {2013},
   url = {http://arxiv.org/abs/1309.7476},
   Abstract = {In an atomic, cancellative, commutative monoid, the
             omega-value measures how far an element is from being prime.
             In numerical monoids, we show that this invariant exhibits
             eventual quasilinearity (i.e., periodic linearity). We apply
             this result to describe the asymptotic behavior of the
             omega-function for a general numerical monoid and give an
             explicit formula when the monoid has embedding dimension
             2.},
   Key = {fds221103}
}


%% Papers Submitted   
@article{fds219347,
   Author = {J. Haarmann and A. Kalauli and A. Moran and C. O'Neill and R.
             Pelayo},
   Title = {Factorization Properties of Leamer Monoids},
   Journal = {Semigroup Forum},
   Year = {2013},
   url = {http://arxiv.org/abs/1309.7477},
   Abstract = {The Huneke-Wiegand conjecture has prompted much recent
             research in Commutative Algebra. In studying this conjecture
             for certain classes of rings, Garcia-Sanchez 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.},
   Key = {fds219347}
}