When Are There Infinitely Many Irreducible Elements in a Principal Ideal Domain?

Publications in Refereed Journals 1. I numeri di Fermat, Periodico di Matematiche, VII, 5 (1998), no. 2-3, 63–68 2. Some observations on the statistical independence and the distribution of zeros in the Selberg Class, Rend. Circ. Mat. Palermo (2), 52 (2003), no. 2, 211–223 3. Extending the idea of compressed algebra to arbitrary socle-vectors, J. Algebra 270 (2003), no. 1, 181–198 4. When are There Infinitely Many Irreducible Elements in a Principal Ideal Domain?, Amer. Math. Monthly 111 (2004), no. 2, 150–152 5. Extending the idea of compressed algebra to arbitrary socle-vectors, II: cases of nonexistence, J. Algebra 275 (2004), no. 2, 730–748 6. Stanley’s theorem on codimension 3 Gorenstein h-vectors, Proc. Amer. Math. Soc. 134 (2006), no. 1, 5–8 7. Level algebras of type 2, Comm. Algebra 34 (2006), no. 2, 691–714 8. When is there a unique socle-vector associated to a given h-vector?, Comm. Algebra 34 (2006), no. 5, 1847–1860 9. A non-unimodal codimension 3 level h-vector, J. Algebra 305 (2006), no. 2, 949–956 10. Improving the bounds of the Multiplicity Conjecture: the codimension 3 level case, J. Pure Appl. Algebra 209 (2007), no. 1, 79–89 11. Partial derivatives of a generic subspace of a vector space of forms: quotients of level algebras of arbitrary type, Trans. Amer. Math. Soc. 359 (2007), no. 6, 2675–2686 12. (with J. Migliore) The Hilbert functions which force the Weak Lefschetz Property, J. Pure Appl. Algebra 210 (2007), no. 2, 465–471 13. The h-vector of a relatively compressed level algebra, Comm. Algebra 35 (2007), no. 4, 1087–1091 14. (with M. Boij) Level Algebras with Bad Properties, Proc. Amer. Math. Soc. 135 (2007), no. 9, 2713–2722 15. (with J. Migliore and U. Nagel) An improved Multiplicity Conjecture for codimension three Gorenstein algebras, Comm. Algebra 36 (2008), no. 1, 112–119 16. (with J. Migliore and U. Nagel) A characterization of Gorenstein Hilbert functions in codimension four with small initial degree, Math. Res. Lett. 15 (2008), no. 2, 331–349 17. (with J. Migliore and U. Nagel) On the degree two entry of a Gorenstein h-vector and a conjecture of Stanley, Proc. Amer. Math. Soc. 136 (2008), no. 8, 2755–2762 18. (with J. Migliore) The strength of the Weak Lefschetz Property, Illinois J. Math. 52 (2008), no. 4, 1417–1433 19. (with J. Migliore and U. Nagel) Bounds and asymptotic minimal growth for Gorenstein Hilbert functions, J. Algebra 321 (2009), no. 5, 1510–1521 20. (with J. Zylinski) Forcing the Strong Lefschetz and the Maximal Rank Properties, J. Pure Appl. Algebra 213 (2009), no. 6, 1026–1030 21. Interval Conjectures for level Hilbert functions, J. Algebra 321 (2009), no. 10, 2705–2715 22. (with M. Boij) Some algebraic consequences of Green’s hyperplane restriction theorems, J. Pure Appl. Algebra 214 (2010), no. 7, 1263–1270 23. (with A. Van Tuyl) Simplicial complexes and Macaulay’s inverse systems, Math. Z. 265 (2010), no. 1, 151–160