William Smith's Home Page

William Smith

I am a Professor in the Mathematics Department.


Lubbock Christian College
Southeastern State College (Oklahoma) B.S. in Ed, 1961
Louisiana State University M.S. (1963), Ph.D. (1965)

Academic Positions Held

University of North Carolina at Chapel Hill

Professor Emeritus (2009 Present)
    Professor (1979 - 2009)
    Associate Professor (1971 - 1979)
    Assistant Professor (1965 - 1971)
    Mathematics Department Chair (1976 - 1981)
    Special Assistant to the Provost (1996 - 1999)
    Associate Provost for Academic Affairs (1999 - 2000)
    Mathematics Department Interim Chair (1/1/2005 - 6/30/2005)


How to find me.

My research interests

Research interests center around general problems in commutative ring theory. Earlier work focused on Prufer and Dedekind domains. Recent work has been in the areas of rings of integer-valued polynomials and factorization of elements in commutative rings and monoids.


American Mathematical Society
Mathematical Association of America
North Carolina Council of Mathematics Teachers
American Association of University Professors
Phi Kappa Phi

Recent Publications and Preprints

  1. (with Chapman, S. and Freeze, M.) "On Generalized Lengths of Factorizations in Dedekind and Krull Domains," Non-Noetherian Commutative Ring Theory (Chapter 6), Kluwer Academic Publishers (2000)
  2. (with Chapman, S.) "An Arithmetical Characterization of Finite Elementary 2-Groups" Communications in Algebra, 29 (2001) 1249-1257
  3. (with Chapman, S. and Freeze, M.) "Equivalence Classes of Minimal Zero-Sequences Modulo a Prime," Ideal Theoretic Methods in Commutative Algebra Lecture Notes in Pure and Applied Mathematics, Marcel Deker,220 (2001)
  4. (with Chapman, S. and Loper, A.) "The Strong Two-Generator Property in Rings of Integer-Valued Polynomials Determined by Finite Sets," Archiv der Mathematik, 78 (2002) 97-105
  5. (with Freeze, M.) "Sumsets of Zerofree Sequences," Arabian J. for Science and Engineering, 26 (2001) 97-105
  6. (with Chapman, S. and Loper, A.) "Strongly Two-generated Ideals in Rings of Integer-valued Polynomials Determined by Finite Sets" CR Math Rep Acad Sci Canada 26(2004)33-38.
  7. (with Chapman, S.) "On Factorization in Block Monoids Formed by {1,a} in Z mod n" Proc Edinburgh Math Soc, 46(2003)257-267
  8. (with Chapman, S., Freeze, M., Gao, WD) "On Davenport's Constant of Finite Abeliam Groups" Far East J Math Sci, 5(2002) 47-54
  9. (with Chapman, S.) "Restricted Elasticity and Rings of Integer-Valued Polynomials Determined by Finite Sets",  Monatshefte fur Mathematik, 148(2006) 195-203
  10. (with Chapman, S.) "A Characterization of Minimal Zero Sequences of Index One in a Finite Cyclic Group", Integers 5(2005)#A27
  11. (with Chang, S., Chapman, S.) "Elasticity in Certain Block Monoids Via the Euclidean Table"  Mathematica Slovaca 57(2007)415-454
  12. (with Chapman, S., Ponomarenko, V) "Robert Gilmer's Contributions to the Theory of Integer-Valued Polynomials"  Multiplicative Ideal Theory in Commutative Algebra,  Springer Pub.Company (2006) 109 - 122
  13. (with Coykendall, J.) "On Unique Factorization Domains" (submitted)
  14. (with Chapman, S.) "An Inequality Concerning the Elasticity of Krull Monoids with Divisor Class Group Z mod p"  Ricerche di Matematica 56(2007)107-117
  15. (with Chang, S., Chapman, S.) "On Minimum Delta Set Values in Block Monoids Over Cyclic Groups" The Ramamujan Journal 14(2007) 155-171.
  16. (with Chapman, S., Schmid, W.) "Quasi-Half-Factorial Subsets of Abelian Torsion Groups" Houston J. Math. 35(2009)13-22.
  17. (with Chapman, S. & Schmid, W.) "On Minimal Distances in Krull Monoids withInfinite Class Group" Bull Lon Math Soc 40(2008)613-618.
  18. (with Anderson, D.F., Chapman, S.) "On a Property of the Division Algorithm and its Application to the Theory of Non-Unique Factorizations" (accepted -- Elemente der Mathematik)

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Last modified: 13 August 2009