Publications

Refereed Research Papers

[39] Factorization theory of root closed monoids of small rank (with Jim Coykendall), Communications in Algebra, 20 pages (to appear)
[38] Polynomial and power series rings with finite quotients (with
Adam Salminen), Houston Journal of Mathematics, 8 pages (to appear)
[37] Residually small commutative rings (with
Adam Salminen), Journal of Commutative Algebra, 17 pages (to appear)
[
36]
Turning automatic continuity around: automatic homomorphisms (with Ryan Berndt), Real Analysis Exchange, 16 pages (to appear)
[35]
Divisible multiplicative groups of fields, Journal of Algebra 453 (2016), 177-188.
[34] The axiomatizability of the class of root closed monoids (with Alan Loper and Nick Werner), Semigroup Forum 91 (2015), no. 3, 737-740.
[33] The theory of integrally closed domains is not finitely axiomatizable, Mathematical Logic Quarterly 61 (2015), no. 1-2, 120-122.
[32] A note on strongly Jonsson binary relational structures, Algebra Universalis 73 (2015), no. 1, 97-101.
[31] Strongly Jonsson and strongly HS modules, Journal of Pure and Applied Algebra 218 (2014), no. 8, 1385-1399.
[30] Commutative rings with infinitely many maximal subrings (with Alborz Azarang), Journal of Algebra and Its Applications 13 (2014), no. 6, 1450037, 29 pp.
[29] Small and large ideals of an associative ring, Journal of Algebra and Its Applications 13 (2014), no. 5, 1350151, 20 pp.
[28] Modules which are isomorphic to their factor modules (with Adam Salminen), Communications in Algebra 41 (2013), no. 4, 1300-1315.
[27] Jonsson posets and unary Jonsson algebras (with Keith Kearnes), Algebra Universalis 69 (2013), no. 3, 101-112.
[26] Rings whose multiplicative endomorphisms are power functions, Semigroup Forum 86 (2013), no. 2, 272-278.
[25] Rings which admit faithful torsion modules II (with Ryan Schwiebert), Journal of Algebra and Its
Applications 11 (2012), no. 3, 1250054, 12 pp.
[24] Rings which admit faithful torsion modules (with Ryan Schwiebert), Communications in Algebra 40 (2012), no. 6, 2184-2198.
[23] On modules whose proper homomorphic images are of smaller cardinality (with Adam Salminen), Canadian Mathematical Bulletin 55 (2012), no. 2, 378-389.
[22] On elementarily k-homogeneous unary structures, Forum Mathematicum 23 (2011), no. 4, 791-802.
[21] Cardinalities of residue fields of Noetherian integral domains (with Keith Kearnes), Communications in Algebra 38 (2010), no. 10, 3580-3588.
[20] Jonsson modules over Noetherian rings, Communications in Algebra 38 (2010), no. 9, 3489-3498.
[19] On the axiom of union, Archive for Mathematical Logic 49 (2010), no. 3, 283-289.
[18] More results on congruent modules, Journal of Pure and Applied Algebra 213 (2009), no. 11, 2147-2155.
[17] On modules M for which N~M for every submodule N of size |M|, Journal of Commutative Algebra 1 (2009), no. 4, 679-699.
[16] Ring semigroups whose subsemigroups intersect, Semigroup Forum 79 (2009), no. 2, 413-416.
[15] Ring semigroups whose subsemigroups form a chain, Semigroup Forum 78 (2009), no. 2, 371-374.
[14] Some results on Jonsson modules over a commutative ring, Houston Journal of Mathematics 35 (2009), no. 1, 1-12.
[13] On infinite modules M over a Dedekind domain for which N~M for every submodule N of cardinality |M|, Rocky Mountain Journal of Mathematics 39 (2009), no. 1, 259-270.
[12] A note on the n-generator property for commutative monoids, Semigroup Forum 74 (2007), no. 1,155-158.

Refereed Survey Papers

[11] Unifying some notions of infinity in ZC and ZF, Reports on Mathematical Logic, 10 pages (to appear)
[10] Jonsson and HS modules over commutative rings, International Journal of Mathematics and Mathematical Sciences (2014), 120907, 13 pp.

Miscellaneous Refereed Publications

[9] I'm thinking of a number... (with Adam Hammett), Missouri Journal of Mathematical Sciences, 16 pages (to appear)
[8] Game show shenanigans: Monty Hall meets mathematical logic (with Greg Morrow and Adam Salminen), Elemente der Mathematik, 11 pages (to appear)
[7] A characterization of the cyclic groups by subgroup indices (with Victoria Slattum), College Mathematics Journal 47 (2016), no. 1, 29-33.
[6] The converse of the Intermediate Value Theorem: from Conway to Cantor to cosets and beyond, Missouri Journal of Mathematical Sciences 26 (2014), no. 2, 134-150.
[5] Groups whose subgroups have distinct cardinalities, Pi Mu Epsilon Journal 14 (2014), no. 1, 31-37.
[4] Group permutations which preserve subgroups (with Veronica Marth), Pi Mu Epsilon Journal 13 (2012), no. 7, 407-414.
[3] The number of homomorphic images of an abelian group, International Journal of Algebra 5 (2011), no. 3, 107-115.
[2] An independent axiom system for the real numbers, College Mathematics Journal 40 (2009), no. 2,78-86.

Book Chapter

[1] Jonsson modules over commutative rings, Chapter 1 of "Commutative Rings: New Research", Nova Science Publishers, New York (2009), 1-6. (invited chapter)

Problems Posed

[37] Problem #???, College Mathematics Journal (to appear)
[36] Problem #???, Pi Mu Epsilon Journal (to appear)
[35] Problem #???, Pi Mu Epsilon Journal (to appear)
[34] Problem #???, Mathematics Magazine (to appear)
[33] Problem #??? (with Adam Salminen), College Mathematics Journal (to appear)
[32] Problem #??? (with Keith Kearnes), College Mathematics Journal (to appear)
[31] Problem #???, College Mathematics Journal (to appear)
[30] Problem #???, College Mathematics Journal (to appear)
[29] Problem #11887 (with Luke Harmon), American Mathematical Monthly 123 (2016), no. 2, p. 197.
[28] Problem #1067, College Mathematics Journal 47 (2016), no. 1, p. 61.
[27] Problem #1054, College Mathematics Journal 46 (2015), no. 3, p. 221.
[26] Problem #326 (with Alan Loper), Math Horizons 23 (2015), no. 1, p. 30.
[25] Problem #318, Math Horizons 22 (2015), no. 3, p. 30.
[24] Problem #11813, American Mathematical Monthly 122 (2015), no. 1, p. 76.
[23] Problem #11750, American Mathematical Monthly 121 (2014), no. 1, p. 83.
[22] Problem #1934, Mathematics Magazine 86 (2013), no. 5, p. 382.
[21] Problem #1011, College Mathematics Journal 44 (2013), no. 5, p. 437.
[20] Problem #1006, College Mathematics Journal 44 (2013), no. 4, p. 325.
[19] Problem #11702, American Mathematical Monthly 120 (2013), no. 4, p. 365.
[18] Problem #985, College Mathematics Journal 43 (2012), no. 4, p. 338.
[17] Problem #11658, American Mathematical Monthly 119 (2012), no. 7, p. 608.
[16] Problem #1900, Mathematics Magazine 85 (2012), no. 3, p. 229.
[15] Problem #977, College Mathematics Journal 43 (2012), no. 3, p. 257.
[14] Problem #968, College Mathematics Journal 43 (2012), no. 1, p. 95.
[13] Problem #11617, American Mathematical Monthly 119 (2012), no. 1, p. 68.
[12] Problem #946, College Mathematics Journal 42 (2011), no. 2, p. 151.
[11] Problem #940, College Mathematics Journal 41 (2010), no. 5, p. 410.
[10] Problem #1211, Pi Mu Epsilon Journal, Fall 2009, p. 560.
[9] Problem #11451, American Mathematical Monthly 116 (2009), no. 7, p. 648.
[8] Problem #1825 (with Kevin Schoenecker), Mathematics Magazine 82 (2009), no. 3, p. 228.
[7] Problem #892, College Mathematics Journal 40 (2009), no. 1, p. 55.
[6] Problem #1810, Mathematics Magazine 81 (2008), no. 5, p. 376.
[5] Problem #871, College Mathematics Journal 39 (2008), no. 2, p. 153.
[4] Problem #11284, American Mathematical Monthly 114 (2007), no. 4, p. 358.
[3] Problem #203, Math Horizons, September 2006, p. 40.
[2] Problem #820, College Mathematics Journal 37 (2006), no. 1, p. 60.
[1] Problem #11166, American Mathematical Monthly 112 (2005), no. 7, p. 654.