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Ricardo Carrera, Ph.D.

Professor
Dept. of Mathematics
(954) 262-8463 ricardo@nova.edu

Education:

  • Ph.D. Mathematics, University of Florida (2004)
  • M.S. Mathematics, University of Florida (2002)
  • B.S.E. Engineering Physics, University of Michigan (1998)
  • B.S. Mathematics, University of Michigan (1998)

Research Interest(s):

  • Ordered Algebraic Structures
  • Category Theory
  • Topology 
  • Cryptography

Courses Taught:

  • Trigonometry
  • Calculus I, II
  • Number Theory
  • Abstract Algebra I, II
 

My research is in the area of ordered algebraic structures and focuses on lattice-ordered groups, topology, category theory and frame-theory. In addition, I am also interested in number theory and cryptography. My current projects:

  • Investigating the complex taxonomy of W-hull classes
  • Investigating the algebraic properties of frames
  • Complemented frames

Peer-reviewed publications:

  1. R. E. Carrera, Generalized Baer Rings, in preparation.
  2. R. E. Carrera and A. W. Hager, Bounded equivalence of hull classes in archimedean lattice-ordered groups II, in preparation.
  3. R. E. Carrera, Pointfree functorial polar functions II, in preparation.
  4. R. E. Carrera, P-essential mappings in compact normal joinfit frames, in preparation.
  5. R. E. Carrera and A. W. Hager,  Bounded equivalence of hull classes in archimedean lattice-ordered groups with unit, Applied Categorical Structures, 24 (2016), no. 2, 163-179.
  6. R. E. Carrera, Pointfree functorial polar functions, Applied Categorical Structures 24 (2016), no. 1, 37-52.
  7. R. E. Carrera and A. W. Hager, B-saturated hull classes in l-groups and covering classes of spaces, Applied Categorical Structures 23 (2015), no. 5, 709-723.
  8. R. E. Carrera,W. Iberkleid, R. LaFuente, and W. McGovern, acc-Baer rings, Math. Slovaca,  65 (2015), no. 2, 371-386.
  9. R. E. Carrera, Various disconnectivities of spaces and projectabilities of l-groups, Algebra Universalis 68 (2012), no. 1-2, 91-109.
  10. R. E. Carrera and A. W. Hager, On hull classes of l-groups and covering classes of spaces, Math. Slovaca 61 (2011), no. 3, 411-428.
  11. R. E. Carrera, Functorial polar functions, Math. Slovaca 61 (2011), no. 3, 389-410.

Math outreach publications:

  1. Mathematics and Entertainment, Matrix Math Column, no. 9, Nova Southeastern University, November 2013. 
  2. Abstract Algebra and its Applications, Matrix Math Column, no. 5, Nova Southeastern University, November 2012.

To search for publications click on the link below

NSUWorks

  1. Behind the Numbers, Mathematics Colloquium Series, Nova Southeastern University, February 03, 2016, speaker.
  2. 18th Annual Conference on Ordered Algebraic Structures, H.L. Wilkes Honors College Florida Atlantic University, May 8-10th 2015, attended. 
  3. Various completeness of an archimedeal lattice-oredered group, Second Annual Mini-Conference on Commutative Rings, Florida Atlantic University, March 08, 2014, speaker.
  4. Hull Classes in Frames, OAL 13: Conference on Frames and Lattice-Ordered Groups, Penn State Erie, Erie Pennsylvania, June 24-26, 2013, speaker.
  5. Lattice Theory and Commutative Semiprime Rings, Sixth-Annual Farquhar College of Arts and Sciences Faculty Symposium, April 08, 2013, speaker.
  6. Generalized Baer Rings, Mini-Conference on Commutative Rings, Florida Atlantic University, March 09, 2013, speaker.
  7. Math Workshop, University of Florida, January 19-20, 2013, speaker.
  8. Hull Classes vs. Covering Classes, Fifth-Annual Farquhar College of Arts and Sciences Faculty Symposium, April 09, 2012, speaker.
  9. Pointfree polar functions, Frames 12: Frames in Algebra, University of Florida, March 05-07, 2012, speaker.
  10. acc-Baer Rings, University of Florida Math Workshop, June 25, 2011, speaker.
  11. acc-projectability & acc-disconnectivity, University of Florida Math Workshop, June 24, 2011, speaker.
  12. PB-Hulls, Fourth-Annual Farquhar College of Arts and Sciences Faculty Symposium, April 04, 2011, speaker.
  13. l-groups and MV-Algebras: Interaction and Impact on Algebras of Logic, October 13-15, 2010, Buenos Aires, Argentina, attended.
  14. Course Redesign with ALEKS Workshop, Rosen Centre Hotel, March 28, 2010, Orlando, Florida, participant.
  15. Frames vs. Topology Workshop, University of Florida, December 3-5, 2009, participant.
  16. 12th Annual International Conference on Ordered Algebraic Structures, Bowling Green State University, June 15-18, 2009, attended.
  17. MV-algebra vs. Frames Workshop, Bowling Green State University, June 8-12, 2009, participant.
  18. Fifth Annual International Bioinformatics Symposium, Nova Southeastern University, Ft. Lauderdale Florida, May 14-16, 2009, attended.
  19. Reflections, Second-Annual Farquhar College of Arts and Sciences Faculty Symposium, March 23, 2009, speaker.
  20. Conference on the Conrad Legacy, University of Florida, Gainesville Florida, May 5-8, 2008, attended.
  21. Second International Workshop on Matrix Analysis and Applications, Nova Southeastern University, Ft. Lauderdale Florida, December 15-17, 2006, attended.
  22. Lattice-Ordered Groups and f-Rings Conference, University of Florida, Gainesville, Florida, March 9-11, 2006. attended.
  23. Ninth Annual Fall Meeting of the North Carolina Section of American Association of Physics Teachers, Davidson College, Davidson North Carolina, October 29-30, 2004, attended.
  24. Categorical properties of  Wc, Conference in Lattice-Ordered Groups and f-Rings, University of Florida, Gainesville Florida, March 3-6, 2004, speaker.
  25. Reflections in Wk, Sixth-Annual Conference in Ordered Algebraic Structures, Vanderbilt University, Nashville Tennessee, March 5-8, 2003, speaker.
  26. Fifth-Annual Conference in Ordered Algebraic Structures, Vanderbilt University, Nashville Tennessee, March 7-9, 2002, attended.
  27. Fourth-Annual Conference in Ordered Algebraic Structures, University of Florida, Gainesville Florida, February 28-March 3, 2001, attended.
  28. Second-Annual Conference in Ordered Algebraic Structures, University of Florida, Gainesville Florida, March 12-13, 1999, attended.

To search for presentations click on the link below

NSUWorks

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