My research interests (currently) lie mostly in the fields of commutative algebra and algebraic number theory. Below is a list of published papers and projects that I am working on. This list is in (more or less) chronological order. If these tantalizing titles make you salivate, drop me a line.
RESEARCH PUBLICATIONS
[1] The Picard group of a polynomial ring. Zero-dimensional commutative rings; Lecture Notes in Pure and Applied Math, 171 pp.191-200. Click here for a pdf version.
[2] Normsets and determination of unique factorization in rings of algebraic integers. Proc. Amer. Math. Soc.124(1996), no. 6, 1727-1732. Click here for a pdf version.
[3] Properties of the normset relating to the class group. Proc. Amer. Math. Soc.124(1996), no. 12, 3587-3593. Click here for a pdf version.
[4] Formal power series over zero-dimensional SFT-rings.(with J. Condo and D. Dobbs)Comm. Algebra24(1996), no. 8, 2687-2698. Click here for a pdf version.
[5] A characterization of polynomial rings with the half-factorial property. Factorization in integral domains; Lecture Notes in Pure and Applied Math, 189 pp. 291-294. Click here for a pdf version.
[6] Strong convergence properties of SFT-rings.(with J. Condo) Comm. Algebra27(1999), no. 5, 2073-2085. Click here for a pdf version.
[7] The half-factorial property in integral extensions.Comm. Algebra27(1999), no. 7, 3153-3159. Click here for a pdf version.
[8] On integral domains with no atoms. (with D. Dobbs and B. Mullins)Comm. Algebra27(1999), no. 12, 5813-5831. Click here for a pdf version.
[9] Fragmented domains have infinite Krull dimension. (with D. Dobbs) Rend. Circ. Mat. Palermo (2)50(2001), no. 2, 377-388. Click here for a pdf version.
[10] Elasticity properties preserved in the normset. to appear in J. Number Theory. Click here for a pdf version.
[11] A remark on arithmetic equivalence and the normset. Acta Arithmetica92(2000), 105-108.Click here for a pdf version.
[12] Half-factorial domains in quadratic fields. J. Algebra235(2001), 417-430. Click here for a pdf version.
[13] Factorization in antimatter rings. (with B. Mullins and D. Dobbs) Advances in Commutative Ring Theory; Lecture Notes in Pure and Applied Mathematics, 205 pp. 217-226. Click here for a pdf version. (This one is in bad shape, but readable.)
[14] Divisor properties inherited by normsets of rings of integers. (with A. Teymuroglu)Advances in Commutative Ring Theory; Lecture Notes in Pure and Applied Mathematics, 205 pp. 227-239. Click here for a pdf version.
[15] Sets with few intersection numbers from Singer subgroup orbits. (with J. Dover) European J. Combin.22(2001), no. 4, 455-464. Click here for a pdf version.
[16] A homological approach to factorization. preprint.
[17] On zero-dimensionality and fragmented rings. (with D. Dobbs and B. Mullins) Bull. Austral. Math. Soc.60(1999), 137-151. Click here for a pdf version.
[18] On the integral closure of a half-factorial domain. to appear. Click here for a pdf version.
[19] Normset theory for number fields with certain normal closures. in preparation.
[20] Elasticity bounds for norms in quadratic rings of integers. in preparation.
[21] Divisibility conditions that force certain dimension behavior. in preparation.
[22] The SFT property does not imply finite dimension for power series. to appear in J. Algebra. Click here for a pdf version.
[23] On a generalization of the Davenport constant. preprint.
[24] GD(1) and GD(2) are not preserved in integral closures. to appear in the International J. Comm. Rings. Click here for a pdf version.
[25] The half-factorial property in power series rings. preprint.
[26] Survival-pairs of commutative rings have the lying-over property. (with D. Dobbs) to appear Comm. Algebra. Click here for a pdf version.
[27] A generalization of the Hilbert Basis Theorem. preprint.
[28] On the dimension of R[[x]]. in preparation.
[29] AP-domains and unique factorization. (with M. Zafrullah) submitted. Click here for a pdf version.
[30] The half-factorial property and domains of the form A+xB[x]. (with T. Dumitrescu and M. Zafrullah) to appear in the Houston Journal of Mathematics. Click here for a pdf version.
[31] Zero-divisor graphs of polynomials and power series over commutative rings. (with M. Axtell and J. Stickles) submitted. Click here for a pdf version.
[32] On unique factorization domains. (with Bill Smith) preprint. Kinda interesting...it is shown that one of the axioms for UFD is redundant! Click here for a pdf version.
[33] Integral domains having nonzero elements with infinitely many prime divisors. (with T. Dumitrescu) To appear in Comm. Algebra. Click here for a pdf version.
[34] Some remarks on infinite products. To appear. Click here for a pdf version.
[35] Monoid domain constructions of antimatter domains. (with D. D. Anderson, L. Hill, and M. Zafrullah) To appear in Comm. Algebra. Click here for a pdf version.
[36] Finitely generated-fragmented domains. (with T. Dumitrescu) Submitted. Click here for a pdf version.
[37] Irreducible divisor graphs. (with J. Maney) To appear in Comm. Algebra. Click here for a pdf version.
[38] A generalization of integrality. (with T. Dutta) Submitted. Click here for a pdf version.
[39] Atomicity in Certain Pullbacks. (with J. Boynton) Submitted. Click here for a pdf version.
[40] An Embedding Theorem. (with B. Mammenga) To appear in J. Algebra. Click here for a pdf version.
[41] CK-Domains and the Goldbach Conjecture. (with C. Spicer) To appear in Proc. Amer. Math. Soc. Click here for a pdf version.
SURVEY ARTICLES
[1] Half-factorial domains, a survey. (with S. Chapman) in Non-Noetherian Commutative Ring Theory S. T. Chapman and S. Glaz, eds. Kluwer. Click here for a pdf version.
[2] Extensions of half-factorial domains: a survey. To appear. Click here for a pdf version.