# C.V. & Publications

**CURRICULUM VI**** TA** (

*always current)*

c.v.

*(*

**PUBLICATIONS***below, ** denotes an undergraduate coauthor and * denotes a graduate student coauthor; manuscripts in preparation or under review not listed*)

**Refereed Research Papers**

[60]

*Unifying some classical results on Artinian rings and modules*(with Donovan Leyba** and Zak Mesyan), Communications in Algebra, to appear, 8 pages.

[59]

*From ancient Egyptian fractions to modern algebra*(with Lorenzo Guerrieri and Alan Loper), Journal of Algebra and Its Applications, to appear, 14 pages.

[58]

*A characterization of potent rings*, Glasgow Mathematical Journal

**65**(2023), no. 2, 324-327.

[57]

*Almost strongly unital rings*(with Evan Senkoff**), Involve

**16**(2023), no. 3, 453-465.

[56]

*Countably coverable rings*(with Nick Werner), Communications in Algebra

**51**(2023), no. 7, 2748-2758.

[55]

*Unital rings with cardinality restrictions on unital subrings*, Mediterranean Journal of Mathematics

**20**(2023), no. 1, Paper Number 14, 13 pp.

[54]

*Modules whose submodule lattice is lower finite*(with Luke Harmon*), Journal of Algebra and Its Applications

**20**(2021), no. 12, 2150230, 16 pp.

[53]

*A characterization of large Dedekind domains*, Archiv der Mathematik

**115**(2020), no. 2, 159-168.

[52]

*Rings with arithmetical closure properties relative to the prime spectrum and its complement*, Communications in Algebra

**48**(2020), no. 5, 2041-2050.

[51]

*Rings whose subrings have an identity*(with John Stroud**), Involve

**13**(2020), no. 5, 823-828.

[50]

*An infinite cardinal-valued Krull dimension for rings*(with Alan Loper and Zak Mesyan), Journal of Algebra

**517**(2019), 223-248.

[49]

*Infinite sums in totally ordered abelian groups*(with Caitlin Randall** and Logan Robinson**), Involve

**12**(2019), no. 2, 281-300.

[48]

*Residually small commutative rings*(with Adam Salminen), Journal of Commutative Algebra

**10**(2018), no. 2, 187-211.

[47]

*Residual smallness in commutative algebra*(with Adam Salminen), Communications in Algebra

**46**(2018), no. 5, 2109-2122.

[46]

*Rings isomorphic to their nontrivial subrings*(with Jacob Lojewski**), Involve

**11**(2018), no. 5, 877-883.

[45]

*Elementarily lambda-homogeneous binary functions*, Algebra Universalis

**78**(2017), no. 2, 147-157.

[44]

*Factorization theory of root closed monoids of small rank*(with Jim Coykendall), Communications in Algebra

**45**(2017), no. 7, 2795-2808.

[43]

*Polynomial and power series rings with finite quotients*(with Adam Salminen), Houston Journal of Mathematics

**43**(2017), no. 1, 31-38.

[42]

*Turning automatic continuity around: automatic homomorphisms*(with Ryan Berndt), Real Analysis Exchange

**41**(2016), no. 2, 271-286.

[41]

*Unifying some notions of infinity in ZC and ZF*, Reports on Mathematical Logic

**51**(2016), 43-56.

[40]

*Divisible multiplicative groups of fields*, Journal of Algebra

**453**(2016), 177-188.

[39]

*The axiomatizability of the class of root closed monoids*(with Alan Loper and Nick Werner), Semigroup Forum

**91**(2015), no. 3, 737-740.

[38]

*The theory of integrally closed domains is not finitely axiomatizable*, Mathematical Logic Quarterly

**61**(2015), no. 1-2, 120-122.

[37]

*A note on strongly Jonsson binary relational structures*, Algebra Universalis

**73**(2015), no. 1, 97-101.

[36]

*Strongly Jonsson and strongly HS modules*, Journal of Pure and Applied Algebra

**218**(2014), no. 8, 1385-1399.

[35]

*Commutative rings with infinitely many maximal subrings*(with Alborz Azarang), Journal of Algebra and Its

*Applications*

**13**(2014), no. 6, 1450037, 29 pp.

*[34]*

*Small and large ideals of an associative ring*, Journal of Algebra and Its Applications

**13**(2014), no. 5, 1350151, 20 pp.

[33]

*Modules which are isomorphic to their factor modules*(with Adam Salminen), Communications in Algebra

**41**(2013), no. 4, 1300-1315.

[32]

*Jonsson posets and unary Jonsson algebras*(with Keith Kearnes), Algebra Universalis

**69**(2013), no. 3, 101-112.

[31]

*Rings whose multiplicative endomorphisms are power functions*, Semigroup Forum

**86**(2013), no. 2, 272-278.

[30]

*Rings which admit faithful torsion modules II*(with Ryan Schwiebert*), Journal of Algebra and Its Applications

**11**(2012), no. 3, 1250054, 12 pp.

[29]

*Rings which admit faithful torsion modules*(with Ryan Schwiebert*), Communications in Algebra

**40**(2012), no. 6, 2184-2198.

[28]

*On modules whose proper homomorphic images are of smaller cardinality*(with Adam Salminen), Canadian Mathematical Bulletin

**55**(2012), no. 2, 378-389.

[27]

*On elementarily kappa-homogeneous unary structures*, Forum Mathematicum

**23**(2011), no. 4, 791-802.

[26]

*Cardinalities of residue fields of Noetherian integral domains*(with Keith Kearnes), Communications in Algebra

**38**(2010), no. 10, 3580-3588.

[25]

*Jonsson modules over Noetherian rings*, Communications in Algebra

**38**(2010), no. 9, 3489-3498.

[24]

*On the axiom of union*, Archive for Mathematical Logic

**49**(2010), no. 3, 283-289.

[23]

*More results on congruent modules*, Journal of Pure and Applied Algebra

**213**(2009), no. 11, 2147-2155.

[22]

*On modules M for which N~M for every submodule N of size |M|*, Journal of Commutative Algebra

**1**(2009), no. 4, 679-699.

[21]

*Ring semigroups whose subsemigroups intersect*, Semigroup Forum

**79**(2009), no. 2, 413-416.

[20]

*Ring semigroups whose subsemigroups form a chain*, Semigroup Forum

**78**(2009), no. 2, 371-374.

[19]

*Some results on Jonsson modules over a commutative ring*, Houston Journal of Mathematics

**35**(2009), no. 1, 1-12.

[18]

*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.

[17]

*A note on the n-generator property for commutative monoids*, Semigroup Forum

**74**(2007), no. 1,155-158.

**Miscellaneous Refereed Papers**

[16]

*Getting to the root of the root law for limits*(with Van Hovenga**), International Journal of Mathematical Education in Science and Technology

**53**(2022), no. 11, 3162-3165.

[15]

*Calculating complex cosine clusters*(with Niles Johnson and Alan Loper), Pi Mu Epsilon Journal

**15**(2022), no. 7, 405-414.

[14]

*Problem-posing: a look behind the scenes*, Pi Mu Epsilon Journal

**15**(2020), no. 1, 111-118.

[13]

*A short proof of the Bolzano-Weierstrass Theorem*(with Katrina Biele**), College Mathematics Journal

**48**(2017), no. 4, 288-289.

[12]

*A radical excursion: from irrational roots to Prufer domains and back*(with Ben Griffith**), Pi Mu Epsilon Journal,

**14**(2016), no. 5, 327-332.

[11]

*Game show shenanigans: Monty Hall meets mathematical logic*(with Greg Morrow and Adam Salminen), Elemente der Mathematik

**71**(2016), no. 4, 145-155.

[10]

*I’m thinking of a number…*(with Adam Hammett ), Missouri Journal of Mathematical Sciences

**28**(2016), no. 1, 31-48.

[9]

*A characterization of the cyclic groups by subgroup indices*(with Victoria Slattum**), College Mathematics Journal

**47**(2016), no. 1, 29-33.

[8]

*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.

[7]

*Jonsson and HS modules over commutative rings*, International Journal of Mathematics and Mathematical Sciences (2014), 120907, 13 pp.

[6]

*Groups whose subgroups have distinct cardinalities*, Pi Mu Epsilon Journal

**14**(2014), no. 1, 31-37.

[5]

*Group permutations which preserve subgroups*(with Veronica Marth**), Pi Mu Epsilon Journal

**13**(2012), no. 7, 407-414.

[4]

*The number of homomorphic images of an abelian group*, International Journal of Algebra

**5**(2011), no. 3, 107-115.

[3]

*An independent axiom system for the real numbers*, College Mathematics Journal

**40**(2009), no. 2, 78-86.

[2]

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

**Published Interview**

[1] Alicia Prieto-Langarica,

*A life in search of problems*, Focus, August/September (2022), 26-28. (an interview of myself along with the problem editors of American Mathematical Monthly, Mathematics Magazine, and Math Horizons)

**(Refereed)**

**Problems Posed**

[75]

*Problem #1282*(with Aslanbek Naziev), College Mathematics Journal

**55**(2024), no. 4, p. 352.

[74]

*Problem #1280*(with Aslanbek Naziev), College Mathematics Journal

**55**(2024), no. 3, p. 261.

[73]

*Problem #1271*, College Mathematics Journal

**55**(2024), no. 2, p. 175.

[72]

*Problem #1269*, College Mathematics Journal

**55**(2024), no. 1, p. 65.

[71]

*Problem #1256*, College Mathematics Journal

**54**(2023), no. 4, p. 400.

[70]

*Problem #1248*, College Mathematics Journal

**54**(2023), no. 2, pp. 147-148,

[69]

*Problem #1235*, College Mathematics Journal

**53**(2022) no. 4, p. 320.

[68]

*Problem #1228*, College Mathematics Journal

**53**(2022) no. 3, p. 237.

[67]

*Problem #1219*, College Mathematics Journal

**53**(2022) no. 1, p. 70.

[66]

*Problem #1215*, College Mathematics Journal,

**52**(2021), no. 5, p. 388.

[65]

*Problem*#

*1210*, College Mathematics Journal

**52**(2021), no. 4, p. 307.

[64]

*Problem #1198*(with Alan Loper), College Mathematics Journal

**52**(2021), no. 2, p. 142.

[63]

*Problem #1192*, College Mathematics Journal

**52**(2021), no. 1, p. 64.

[62]

*Problem #1185*, College Mathematics Journal

**51**(2020), no. 4, p. 306.

[61]

*Problem #1179*, College Mathematics Journal

**51**(2020), no. 3, p. 246.

[60]

*Problem #1173*, College Mathematics Journal

**51**(2020), no. 2, pp. 146-147.

[59]

*Problem #1166*, College Mathematics Journal

**51**(2020), no. 1, p. 66.

[58]

*Problem #1356*(with Ikko Saito), Pi Mu Epsilon Journal, Spring 2019.

[57]

*Problem #1155*, College Mathematics Journal

**50**(2019), no. 3, p. 225.

[56]

*Problem #1150*, College Mathematics Journal

**50**(2019), no. 2, p. 144.

[55]

*Problem #1088*(with Luke Harmon*), Mathematics Magazine

**92**(2019), no. 1, p. 73.

[54]

*Problem #1145*, College Mathematics Journal

**50**(2019), no. 1, p. 62.

[53]

*Problem #12089*(with Adam Salminen), American Mathematical Monthly

**126**(2019), no. 1, p. 83.

[52]

*Problem #1140*, College Mathematics Journal

**49**(2018), no. 5, p. 372.

[51]

*Problem #1334*, College Mathematics Journal

**49**(2018), no. 4, p. 296.

[50]

*Problem #12036*, American Mathematical Monthly

**125**(2018), no. 4, p. 370.

[49]

*Problem #2043*(with Adam Salminen), Mathematics Magazine

**91**(2018), no. 2, p. 151.

[48]

*Problem #1125*, College Mathematics Journal

**49**(2018), no. 2, p. 141.

[47]

*Problem #1078*, Mathematics Magazine

**91**(2018), no. 1, p. 72.

[46]

*Problem #1118*(with Logan Robinson**), College Mathematics Journal

**49**(2018), no. 1, p. 61.

[45]

*Problem #12010*(with Adam Salminen), American Mathematical Monthly

**124**(2017), no. 10, p. 971.

[44]

*Problem #1111*, College Mathematics Journal

**48**(2017), no. 5, p. 370.

[43]

*Problem #1106*, College Mathematics Journal

**48**(2017), no. 4, p. 292.

[42]

*Problem #2019*, Mathematics Magazine

**90**(2017), no. 2, p. 145.

[41]

*Problem #353*(with Adam Hammett), Math Horizons

**23**(2017), no. 3, p. 30.

[40]

*Problem #1104*, College Mathematics Journal

**48**(2017), no. 3, p. 220.

[39]

*Problem #1103*, College Mathematics Journal

**48**(2017), no. 3, p. 220.

[38]

*Problem #1332*, Pi Mu Epsilon Journal, Spring 2017.

[37]

*Problem #1331*, Pi Mu Epsilon Journal, Spring 2017.

[36]

*Problem #1096*(with Adam Salminen), College Mathematics Journal

**48**(2017), no. 2, p. 138.

[35]

*Problem #1095*(with Keith Kearnes), College Mathematics Journal

**48**(2017), no. 1, p. 59.

[34]

*Problem #1093*, College Mathematics Journal

**48**(2017), no. 1, p. 58.

[33]

*Problem #2009*, Mathematics Magazine

**89**(2016), no. 5, p. 379.

[32]

*Problem #11943*(with Keith Kearnes), American Mathematical Monthly

**123**(2016), no. 10, p. 1050.

[31]

*Problem #1078*, College Mathematics Journal

**43**(2016), no. 3, pp. 221-222.

[30]

*Problem #1998*, Mathematics Magazine

**89**(2016), no. 3, pp. 223-224.

[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 #11658*, American Mathematical Monthly

**119**(2012), no. 7, p. 608.

[17]

*Problem #985*, College Mathematics Journal

**43**(2012), no. 4, p. 338.

[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.

[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,

**14**(2006), no. 1, 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.