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Edmond W. H. Lee, Ph.D.

Associate Professor
Dept. of Mathematics
(954) 262-8320 elee1@nova.edu

Education: 

  • Ph.D., Simon Fraser University, 2002 
  • M.Sc., Simon Fraser University, 1997
  • B.Sc., University of Toronto, 1994  

Research Interest(s): 

  • Varieties of semigroups
  • Lattices of varieties
  • Finite basis problem   

Courses Taught:

  • MATH 1030 Intermediate Algebra
  • MATH 1040 Algebra for College Students
  • MATH 1200 Precalculus Algebra 
  • MATH 2100 Calculus I 

Graduate Students:

  • J. R. Pereira, Ph.D. candidate, Universidade Aberta, Lisbon, Portugal
  • W. T. Zhang, Ph.D. 2009, Lanzhou University, Gansu, P. R. China

Some current investigations: 

  • Varieties of semigroups with involution 
  • Join irreducible pseudovarieties 
  • Classification of varieties generated by semigroups of small order
  1. E. W. H. Lee, Finite involution semigroups with infinite irredundant bases of identities, Forum Mathematicum 28 (2016), no. 3, 587-607.
  2. E. W. H. Lee, Finitely based finite involution semigroups with non-finitely based reducts, Quaestiones Mathematicae 39 (2016), no. 2, 217-243.
  3. E. W. H. Lee, A class of finite semigroups without irredundant bases of identities, Yokohama Mathematical Journal 61 (2015), 1–28.
  4. E. W. H. Lee, Inherently non-finitely generated varieties of aperiodic monoids with central idempotents, Journal of Mathematical Sciences 209 (2015), no. 4, 588–599.
  5. E. W. H. Lee and J. R. Li, The variety generated by all monoids of order four is finitely based, Glasnik Matematički. Serija III 50 (2015), no. 2, 373–396.
  6. E. W. H. Lee and W. T. Zhang, Finite basis problem for semigroups of order six, LMS Journal of Computation and Mathematics 18 (2015), no. 1, 1–129.
  7. E. W. H. Lee, On a question of Pollák and Volkov regarding hereditarily finitely based identities, Periodica Mathematica Hungarica 68 (2014), no. 2, 128–134.
  8. E. W. H. Lee, On certain Cross varieties of aperiodic monoids with commuting idempotents, Results in Mathematics 66 (2014), no. 3–4, 491–510.
  9. E. W. H. Lee and W. T. Zhang, The smallest monoid that generates a non-Cross variety (in Chinese), Xiamen Daxue Xuebao Ziran Kexue Ban 53 (2014), no. 1, 1–4.
  10. E. W. H. Lee, Almost Cross varieties of aperiodic monoids with central idempotents, Beiträge zur Algebra und Geometrie 54 (2013), no. 1, 121–129.
  11. E. W. H. Lee, Finite basis problem for semigroups of order five or less: generalization and revisitation, Studia Logica 101 (2013), no. 1, 95–115.
  12. E. W. H. Lee, Finitely based monoids obtained from non-finitely based semigroups, Universitatis Iagellonicae Acta Mathematica 51 (2013), 45–49.
  13. E. W. H. Lee, Finite basis problem for the direct product of some J-trivial monoid with groups of finite exponent, Vestnik St. Petersburg State University. Series 1. Mathematics. Mechanics. Astronomy 2013, no. 4, 60–64.
  14. E. W. H. Lee, A sufficient condition for the non-finite basis property of semigroups, Monatshefte für Mathematik 168 (2012), no. 3–4, 461–472.
  15. E. W. H. Lee, Maximal Specht varieties of monoids, Moscow Mathematical Journal 12 (2012), no. 4, 787–802.
  16. E. W. H. Lee, Varieties generated by 2-testable monoids, Studia Scientiarum Mathematicarum Hungarica 49 (2012), no. 3, 366–389.
  17. E. W. H. Lee, J. R. Li, and W. T. Zhang, Minimal non-finitely based semigroups, Semigroup Forum 85 (2012), no. 3, 577–580.
  18. E. W. H. Lee, Cross varieties of aperiodic monoids with central idempotents, Portugaliae Mathematica 68 (2011), no. 4, 425–429.
  19. E. W. H. Lee, Finite basis problem for 2-testable monoids, Central European Journal of Mathematics 9 (2011), no. 1, 1–22.
  20. E. W. H. Lee and J. R. Li, Minimal non-finitely based monoids, Dissertationes Mathematicae 475 (2011), 65 pp.
  21. E. W. H. Lee and M. V. Volkov, Limit varieties generated by completely 0-simple semigroups, International Journal of Algebra and Computation 21 (2011), no. 1–2, 257–294.
  22. C. C. Edmunds, E. W. H. Lee, and K. W. K. Lee, Small semigroups generating varieties with continuum many subvarieties, Order 27 (2010), no. 1, 83–100.
  23. E. W. H. Lee, Combinatorial Rees–Sushkevich varieties that are Cross, finitely generated, or small, Bulletin of the Australian Mathematical Society 81 (2010), no. 1, 64–84.
  24. E. W. H. Lee, On a semigroup variety of György Pollák, Novi Sad Journal of Mathematics 40 (2010), no. 3, 67–73.
  25. E. W. H. Lee, Finitely generated limit varieties of aperiodic monoids with central idempotents, Journal of Algebra and Its Applications 8 (2009), no. 6, 779–796.
  26. E. W. H. Lee, Hereditarily finitely based monoids of extensive transformations, Algebra Universalis 61 (2009), no. 1, 31–58.
  27. E. W. H. Lee, Lyndon's groupoid generates a small almost Cross variety, Algebra Universalis 60 (2009), no. 2, 239–246.
  28. S. I. Kublanovsky, E. W. H. Lee, and N. R. Reilly, Some conditions related to the exactness of Rees–Sushkevich varieties, Semigroup Forum 76 (2008), no. 1, 87–94.
  29. E. W. H. Lee, Combinatorial Rees–Sushkevich varieties are finitely based, International Journal of Algebra and Computation 18 (2008), no. 5, 957–978.
  30. E. W. H. Lee, On the variety generated by some monoid of order five, Acta Scientiarum Mathematicarum 74 (2008), no. 3–4, 509–537.
  31. E. W. H. Lee and N. R. Reilly, Centrality in Rees–Sushkevich varieties, Algebra Universalis 58 (2008), no. 2, 145–180.
  32. E. W. H. Lee, Minimal semigroups generating varieties with complex subvariety lattices, International Journal of Algebra and Computation 17 (2007), no. 8, 1553–1572.
  33. E. W. H. Lee, On a simpler basis for the pseudovariety EDS, Semigroup Forum 75 (2007), no. 2, 477–479.
  34. E. W. H. Lee, On identity bases of exclusion varieties for monoids, Communications in Algebra 35 (2007), no. 7, 2275–2280.
  35. E. W. H. Lee, On the complete join of permutative combinatorial Rees–Sushkevich varieties, International Journal of Algebra 1 (2007), no. 1–4, 1–9.
  36. E. W. H. Lee and M. V. Volkov, On the structure of the lattice of combinatorial Rees–Sushkevich varieties, in: Semigroups and Formal Languages, 164–187, World Scientific, Singapore (2007)
  37. E. W. H. Lee, Maximal normal orthogroups in rings containing no infinite semilattices, Communications in Algebra 34 (2006), no. 1, 323–334.
  38. E. W. H. Lee, Subvarieties of the variety generated by the five-element Brandt semigroup, International Journal of Algebra and Computation 16 (2006), no. 2, 417–441.
  39. E. W. H. Lee, Maximal Clifford semigroups of matrices, Sarajevo Journal of Mathematics 2 (2006), no. 2, 147–152.
  40. E. W. H. Lee and N. R. Reilly, The intersection of pseudovarieties of central simple semigroups, Semigroup Forum 73 (2006), no. 1, 75–94.
  41. E. W. H. Lee, Identity bases for some non-exact varieties, Semigroup Forum 68 (2004), no. 3, 445–457.
  1. Identities satisfied by involution semigroups, Workshop on Groups and Semigroups, University of Porto, June 9, 2015, invited speaker.
  2. Limit varieties generated by completely 0-simple semigroups, The 3rd Novi Sad Algebraic Conference, University of Novi Sad, August 17–21, 2009, invited speaker.
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