Greg Oman

**Refereed Research Papers**

**[33] ***Turning automatic continuity around: automatic homomorphisms* (with Ryan Berndt), Real Analysis Exchange, 16 pages (to appear)

[32] *The axiomatizability of the class of root closed monoids* (with Alan Loper and Nick Werner), Semigroup Forum **91** (2015), no. 3, 737-740.

[31] *The theory of integrally closed domains is not finitely axiomatizable*, Mathematical Logic Quarterly **61** (2015), no. 1-2, 120-122.

[30] *A note on strongly Jonsson binary relational structures*, Algebra Universalis **73** (2015), no. 1, 97-101.

[29] *Strongly Jonsson and strongly HS modules*, Journal of Pure and Applied Algebra **218** (2014), no. 8, 1385-1399.

[28] *Commutative rings with infinitely many maximal subrings* (with Alborz Azarang), Journal of Algebra and Its Applications **13** (2014), no. 6, 1450037, 29 pp.

[27] *Small and large ideals of an associative ring*, Journal of Algebra and Its Applications **13** (2014), no. 5, 1350151, 20 pp.

[26] *Modules which are isomorphic to their factor modules* (with Adam Salminen), Communications in Algebra **41** (2013), no. 4, 1300-1315.

[25] *Jonsson posets and unary Jonsson algebras* (with Keith Kearnes), Algebra Universalis **69** (2013), no. 3, 101-112.

[24] *Rings whose multiplicative endomorphisms are power functions*, Semigroup Forum **86** (2013), no. 2, 272-278.

[23] *Rings which admit faithful torsion modules II *(with Ryan Schwiebert), Journal of Algebra and Its Applications **11** (2012), no. 3, 1250054, 12 pp.

[22] *Rings which admit faithful torsion modules* (with Ryan Schwiebert), Communications in Algebra **40 **(2012), no. 6, 2184-2198.

[21] *On modules whose proper homomorphic images are of smaller cardinality* (with Adam Salminen), Canadian Mathematical Bulletin **55** (2012), no. 2, 378-389.

[20] *On elementarily k-homogeneous unary structures*, Forum Mathematicum **23** (2011), no. 4, 791-802.

[19] *Cardinalities of residue fields of Noetherian integral domains* (with Keith Kearnes), Communications in Algebra **38** (2010), no. 10, 3580-3588.

[18] *Jonsson modules over Noetherian rings*, Communications in Algebra **38** (2010), no. 9, 3489-3498.

[17] *On the axiom of union*, Archive for Mathematical Logic **49** (2010), no. 3, 283-289.

[16] *More results on congruent modules*, Journal of Pure and Applied Algebra **213** (2009), no. 11, 2147-2155.

[15] *On modules M for which N~M for every submodule N of size |M|*, Journal of Commutative Algebra **1** (2009), no. 4, 679-699.

[14] *Ring semigroups whose subsemigroups intersect*, Semigroup Forum **79** (2009), no. 2, 413-416.

[13] *Ring semigroups whose subsemigroups form a chain*, Semigroup Forum **78** (2009), no. 2, 371-374.

[12] *Some results on Jonsson modules over a commutative ring*, Houston Journal of Mathematics **35** (2009), no. 1, 1-12.

[11] *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.

[10] *A note on the n-generator property for commutative monoids*, Semigroup Forum **74** (2007), no. 1,155-158.

**Miscellaneous Refereed Publications**

[9] *Game show shenanigans: Monty Hall meets mathematical logic *(with Greg Morrow and Adam Salminen), Elemente der Mathematik, 11 pages (to appear)

[8] *A characterization of the cyclic groups by subgroup indexes *(with Victoria Slattum), College Mathematics Journal, 6 pages (to appear)

[7] *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.

[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.

**Book Chapter**

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

**Refereed Survey Paper**

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

**Problems Posed**

[31] *Problem #???*, American Mathematical Monthly (to appear)

[30] *Problem #???*, College Mathematics Journal (to appear)

[29] *Problem #???*, College Mathematics Journal (to appear)

[28] *Problem #???*, College Mathematics Journal (to appear)

[27] *Problem #1054*, College Mathematics Journal **46** (2015), no. 3, p. 221.

[26] *Problem #326*, 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*, 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.

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1420 Austin Bluffs Pkwy, Colorado Springs, CO USA 80918

719-255-8227 (UCCS), 800-990-8227