Abstract
The Munn tree representation for the elements of the free inverse monoid is an elegant and useful tool in the theory of inverse semigroups. It has been the starting point for many of the subsequent developments in this theory. In the present paper we generalize this representation for the elements of the bifree locally inverse semigroup. We will represent each element of the bifree locally inverse semigroup as an undirected tree whose vertices, called blocks, are special vertex-labeled graphs themselves. Another distinctive characteristic of these graphs is that they have different types of edges.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Almeida, J.: Finite Semigroups and Universal Algebra. World Scientific, Singapore (1994)
Auinger, K.: On the bifree locally inverse semigroup. J. Algebra 178, 581–613 (1995)
Auinger, K., Oliveira, L.: On the variety of stricts. Studia Sci. Math. Hungarica 50, 207–241 (2013)
Hall, T.: Identities for existence varieties of regular semigroups. Bull. Aust. Math. Soc. 40, 59–77 (1989)
Jones, P.: Free products of inverse semigroups: a survey, with examples. In: Hall, T., Jones, P., Meakin, J. (eds.) Proceedings of the Monash Conference on Semigroups Theory, 140–156. World Scientific, Singapore (1991)
Kaďourek, J., Szendrei, M.B.: A new approach in the theory of orthodox semigroups. Semigroup Forum 40, 257–296 (1990)
Lawson, M.: Inverse Semigroups, the Theory of Partial Symmetries. World Scientific, Singapore (1998)
Margolis, S., Meakin, J.: Inverse monoids, trees and context-free languages. Trans. Am. Math. Soc. 335, 259–276 (1993)
Meakin, J.: An Invitation to Inverse Semigroup Theory, Ordered Structures and Algebra of Computer Languages, pp. 91–115. World Scientific, Singapore (1993)
Munn, W.D.: Free inverse semigroups. Proc. Lond. Math. Soc. 29, 385–404 (1974)
Nambooripad, K.S.S.: Structure of regular semigroups. I, vol. 22, pp. vii+119. Memoirs of the American Mathematical Society (1979)
Nambooripad, K.S.S.: The natural partial order on a regular semigroup. Proc. Edinburgh Math. Soc. 23, 249–260 (1980)
Nambooripad, K.S.S.: Pseudo-semilattices and biordered sets I. Simon Stevin 55, 103–110 (1981)
Oliveira, L.: The free idempotent generated locally inverse semigroup (preprint)
Pastijn, F., Oliveira, L.: Maximal dense ideal extensions of locally inverse semigroups. Semigroup Forum 72, 441–458 (2006)
Scheiblich, H.: Free inverse semigroups. Semigroup Forum 4, 351–359 (1972)
Scheiblich, H.: Free inverse semigroups. Proc. Am. Math. Soc. 38, 1–7 (1973)
Stephen, J.B.: Presentations of inverse semigroups. J. Pure Appl. Algebra 63, 81–112 (1990)
Yeh, Y.T.: The existence of e-free objects in e-varieties of regular semigroups. J. Algebra 164, 471–484 (1992)
Acknowledgments
This work was partially supported by CMUP (UID/MAT/00144/2013), which is funded by FCT (Portugal) with national (MEC) and European structural funds (FEDER), under the partnership agreement PT2020.
Author information
Authors and Affiliations
Corresponding author
Additional information
Communicated by A. Constantin.
Rights and permissions
About this article
Cite this article
Oliveira, L. A Munn tree type representation for the elements of the bifree locally inverse semigroup. Monatsh Math 183, 653–678 (2017). https://doi.org/10.1007/s00605-016-0952-7
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00605-016-0952-7