Research Interests

Publications

  1. Conjugacy and Least Commutative Congruences in Semigroups, Semigroup Forum, in press (arXiv: 2503.02148).
  2. Unifying some classical results on Artinian rings and modules (with D. Leyba and G. Oman), Comm. Algebra 53 (2025) 723-729 (arXiv: 2407.20488).
  3. Properties of congruence lattices of graph inverse semigroups (with M. Anagnostopoulou-Merkouri and J. D. Mitchell), Internat. J. Algebra Comput. 34 (2024) 371-396 (arXiv: 2108.08277).
  4. Automatic continuity, unique Polish topologies, and Zariski topologies on monoids and clones (with L. Elliott, J. Jonušas, J. D. Mitchell, M. Morayne, and Y. Peresse), Trans. Amer. Math. Soc. 376 (2023) 8023–8093 (arXiv: 1912.07029).
    Earlier version: Topological transformation monoids (arXiv: 1809.04590).
  5. Graded semigroups (with R. Hazrat), Israel J. Math. 253 (2023) 249–319 (arXiv: 2008.01379).
  6. Products and intersections of prime-power ideals in Leavitt path algebras (with K. M. Rangaswamy), J. Algebra Appl. 21 (2022) 2250104, 26 pages (arXiv: 2101.05376).
  7. Products of ideals in Leavitt path algebras (with G. Abrams and K. M. Rangaswamy), Comm. Algebra 48 (2020) 1853-1871 (arXiv: 1908.05805).
  8. Infinite-dimensional triangularizable algebras, Forum Math. 31 (2019) 19–33 (arXiv: 1803.07214).
  9. An infinite cardinal-valued Krull dimension for rings (with K. A. Loper and G. Oman), J. Algebra 517 (2019) 223-248 (arXiv: 1711.08554).
  10. Chains of semiprime and prime ideals in Leavitt path algebras (with G. Abrams, B. Greenfeld, and K. M. Rangaswamy), 1-16, Contemp. Math., 715, Amer. Math. Soc., Providence, RI, 2018 (arXiv: 1712.01803).
  11. Infinite-dimensional triangularization, J. Pure Appl. Algebra 222 (2018) 1529-1547 (arXiv: 1608.08282).
  12. Realizing posets as prime spectra of Leavitt path algebras (with G. Abrams, G. Aranda Pino, and C. Smith), J. Algebra 476 (2017) 267-296 (arXiv: 1512.06771).
  13. Infinite-dimensional diagonalization and semisimplicity (with M. C. Iovanov and M. L. Reyes), Israel J. Math. 215 (2016) 801-855 (arXiv: 1502.05184).
  14. The structure of a graph inverse semigroup (with J. D. Mitchell), Semigroup Forum 93 (2016) 111-130 (arXiv: 1409.4380).
  15. Topological graph inverse semigroups (with J. D. Mitchell, M. Morayne, and Y. Peresse), Topol. Appl. 208 (2016) 106-126 (arXiv: 1306.5388).
  16. Traces on semigroup rings and Leavitt path algebras (with L. Vas), Glasgow Math. J. 58 (2016) 97-118 (arXiv: 1502.03766).
  17. Polynomials of small degree evaluated on matrices, Lin. Multilin. Alg. 61 (2013) 1487-1495 (arXiv: 1212.1925).
  18. Commutator Leavitt path algebras, Algebr. Represent. Theory 16 (2013) 1207-1232 (arXiv: 1205.5319).
  19. The Bergman-Shelah preorder on transformation semigroups (with J. D. Mitchell, M. Morayne, and Y. Peresse), Math. Logic Quart. 58 (2012) 424-433 (arXiv: 1109.2706).
  20. Monoids of injective maps closed under conjugation by permutations, Israel J. Math. 189 (2012) 287-305 (arXiv: 1008.1443).
  21. Simple Lie algebras arising from Leavitt path algebras (with G. Abrams), J. Pure Appl. Algebra 216 (2012) 2302-2313 (arXiv: 1107.3114).
  22. Groups where free subgroups are abundant, J. Algebra 344 (2011) 161-171 (arXiv: 1103.1099).
  23. Conjugation of injections by permutations, Semigroup Forum 81 (2010) 297-324 (arXiv: 1003.2027).
  24. The ideals of an ideal extension, J. Algebra Appl. 9 (2010) 407-431 (arXiv: 0909.0440).
  25. On minimal extensions of rings (with T. J. Dorsey), Comm. Algebra 37 (2009) 3463-3486 (arXiv: 0805.3370).
  26. Generating self-map monoids of infinite sets, Semigroup Forum 75 (2007) 648-675 (arXiv: math/0701198).
  27. Endomorphism rings generated using small numbers of elements, Bull. London Math. Soc. 39 (2007) 290-300 (arXiv: math/0508637).
  28. Commutator rings, Bull. Austral. Math. Soc. 74 (2006) 279-288 (arXiv: math/0509148).
  29. Generating endomorphism rings of infinite direct sums and products of modules, J. Algebra 283 (2005) 364-366 (arXiv: math/0405216).

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