Gene Abrams

Department of Mathematics
University of Colorado Colorado Springs

Email: abrams 'at'

Office: Room 288 EAS Building

Office Phone: (719) 255-3182

Fax: (719) 255-3605

Mailing: UCCS Mathematics
1420 Austin Bluffs Parkway
Colorado Springs CO 80918

UCCS Math Department Home Page

ARCS Center, a.k.a. 'Algebras and Rings in Colorado Springs'

(Includes information about the Colorado Springs Algebra Seminar,
a.k.a. 'Rings and Wings'; click on Seminars)

Background and Professional Information

Full vita available on request
Wikipedia page

Research interests

I am an algebraist, with interest in noncommutative rings and their categories of modules. Since 2005 my primary focus has been on a class of rings called "Leavitt path algebras".

Publications since 2014


Journal Publications:

  • “Connections between Abelian sandpile models and the K-theory of weighted Leavitt path algebras” (with R. Hazrat), to appear, European Journal of Mathematics.
  • “Morita equivalence for graded rings” (with E. Ruiz, M. Tomforde), Journal of Algebra 617, 2023, pp. 79-112.
  • “Realizing corners of Leavitt path algebras as Steinberg algebras, with corresponding connections to graph C*-algebras” (with M. Dokuchaev, T.G. Nam), Journal of Algebra 593, 2022, pp. 72-104.
  • “Injective modules over the Jacobson algebra K < X,Y | XY=1 >” (with F. Mantese, A. Tonolo), Canadian Bulletin of Mathematics 64(2), 2021, pp. 323-339.
  • “A matrix viewpoint for various algebraic extensions” (with P.N. Ánh), Elemente der Mathematik 75, 2020, pp. 1-17.
  • “Products of ideals in Leavitt path algebras” (with Z. Mesyan, K. M. Rangaswamy), Communications in Algebra 48, 2020, pp. 1853-1871.
  • "Corners of Leavitt path algebras of finite graphs are Leavitt path algebras" (with Nam), Journal of Algebra 547, 2020, pp 494-518.
  • "Prufer modules over Leavitt path algebras" (with F. Mantese, A. Tonolo), Journal of Algebra and its Applications 18(8), 2019, 1950154, 28 pages.
  • "Leavitt path algebras of Cayley graphs C_n^j" (with C. Gil Canto, S. Erickson), Mediterranean J. Math. 15:197, 2018, 23 pages.
  • "Leavitt path algebras are Bezout" (with F. Mantese, A. Tonolo), Israel J. Math. 228(1), 2018, pp 53-78.
  • "Chains of Semiprime and Prime Ideals in Leavitt Path Algebras" (with B. Greenfeld, Z. Mesyan, K.M. Rangaswamy), Advances in rings and modules, 1–16, Contemporary Mathematics Series Volume 715, American Mathematical Society Publishers, Providence, RI, 2018. (volume in honor of Bruno Mueller)
  • "Realizing posets as prime spectra of Leavitt path algebras" (with G. Aranda Pino, Z. Mesyan, C. Smith), Journal of Algebra 476, 2017, pp. 267 - 296.
  • "Leavitt path algebras having Unbounded Generating Number" (with T.G. Nam, N.T. Phuc), Journal of Pure and Applied Algebra 221, 2017, pp. 1322 - 1343.
  • "WHAT IS ... a Leavitt path algebra?", Notices of the American Mathematical Society 63(8), 2016, pp. 910-911.
  • "The Leavitt path algebras of generalized Cayley graphs" (with G. Aranda Pino), Mediterranean J. Math 13(1), 2016, pp. 1-27.
  • "Cohn path algebras have Invariant Basis Number" (with M. Kanuni), Communications in Algebra 44, 2016, pp. 371-380.
  • "Extensions of simple modules over Leavitt path algebras" (with F. Mantese, A. Tonolo), Journal of Algebra 431, 2015, pp. 78-106.
  • "Leavitt path algebras: the first decade", Bulletin of Mathematical Sciences 5(1), 2015, pp. 59-120.
  • "Leavitt path algebras of Cayley graphs arising from cyclic groups" (with B. Schoonmaker), Proceedings of the conference "Noncommutative rings and their applications, Lens, France, July 2013", American Mathematical Society Contemporary Mathematics Series Volume 634, 2015, pp. 1-10.
  • "A class of C*-algebras that are prime but not primitive" (with M. Tomforde), Muenster J. Math 7, 2014, pp. 489-514.
  • "The prime spectrum and primitive ideal space of a graph C*-algebra" (with M. Tomforde), International J. Math, 25(7), 2014, pp. 1450070(01) - 1450070(22).
  • "On prime non-primitive von Neumann regular algebras" (with J. Bell, K.M. Rangaswamy), Transactions of the American Mathematical Society 366(5), 2014, 2375-2392.

  • An interesting / mysterious number-theoretic construction

    Seminars / Colloquia since 2014

    (all talks 50 - 60 mins unless otherwise indicated)

    Various Professional Activities since 2010

    Activities related to Mad Veterinarian Puzzles


    Seminars / colloquia:

    Hands-on activities (to various teacher groups and student groups):

    Hobbies and Recreational Pursuits

    UCCS Department of Mathematics
    University of Colorado
    Colorado Springs, CO 80918