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Research Article

Semimodularity in congruence lattices of graph inverse semigroups

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Pages 2623-2632 | Received 04 Jan 2020, Accepted 18 Jan 2021, Published online: 14 Feb 2021

References

  • Abrams, G., Pino, G. A. (2005). The Leavitt path algebra of a graph. J. Algebra 293(2):319–334. DOI: 10.1016/j.jalgebra.2005.07.028.
  • Alali, A., Gilbert, N. D. (2017). Closed inverse subsemigroups of graph inverse semigroups. Commun. Algebra 45(11):4667–4678. DOI: 10.1080/00927872.2016.1277230.
  • Ash, C. J., Hall, T. E. (1975). Inverse semigroups on graphs. Semigroup Forum 11(1):140–145. DOI: 10.1007/BF02195262.
  • Chih, T., Plessas, D. (2017). Graphs and their associated inverse semigroups. Discrete Math. 340(10):2408–2414. DOI: 10.1016/j.disc.2017.05.008.
  • Fofanova, T. S. (1978). General Lattice Theory. Basel-Stuttgart: Birkhauser Verlag.
  • Howie, J. M. (1995). Fundamentals of Semigroup Theory. Oxford: Clarendon Press.
  • Jones, D. G. (2011). Polycyclic monoids and their generalizations. Ph.D. thesis. Heriot-Watt University.
  • Jones, D. G., Lawson, M. V. (2014). Graph inverse semigroups: Their characterization and completion. J. Algebra 409:444–473. DOI: 10.1016/j.jalgebra.2014.04.001.
  • Krieger, W. (2006). On subshifts and semigroups. Bull. London Math. Soc. 38(04):617–624. DOI: 10.1112/S0024609306018625.
  • Kumjian, A., Pask, D., Raeburn, I. (1998). Cuntz-Krieger algebras of directed graphs. Pacific J. Math. 184(1):161–174. DOI: 10.2140/pjm.1998.184.161.
  • Kumjian, A., Pask, D., Raeburn, I., Renault, J. (1997). Graphs, groupoids, and Cuntz-Krieger algebras. J. Funct. Anal. 144(2):505–541. DOI: 10.1006/jfan.1996.3001.
  • Mesyan, Z., Mitchell, J. D. (2016). The structure of a graph inverse semigroup. Semigroup Forum 93(1):111–130. DOI: 10.1007/s00233-016-9793-x.
  • Mesyan, Z., Mitchell, J. D., Morayne, M., Péresse, Y. H. (2016). Topological graph inverse semigroups. Topol. Appl. 208:106–126. DOI: 10.1016/j.topol.2016.05.012.
  • Paterson, A. L. T. (1999). Groupoids, Inverse Semigroups and Their Operator Algebras. Boston: Birkhäuser.
  • Wang, Z. P. (2019). Congruences on graph inverse semigroups. J. Algebra 534:51–64. DOI: 10.1016/j.jalgebra.2019.06.020.

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