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    This article has been cited by the following publications. This list is generated based on data provided by CrossRef.
    Ayyash, Mohammed Abu and Rodaro, Emanuele 2016. Undecidability of the word problem for Yamamura’s HNN-extension under nice conditions. Semigroup Forum, Vol. 93, Issue. 1, p. 86.
    Yamamura, Akihiro 2007. Embedding theorems for HNN extensions of inverse semigroups. Journal of Pure and Applied Algebra, Vol. 210, Issue. 2, p. 521.
    DOMBI, E. R. GILBERT, N. D. and RUŠKUC, N. 2005. FINITE PRESENTABILITY OF HNN EXTENSIONS OF INVERSE SEMIGROUPS. International Journal of Algebra and Computation, Vol. 15, Issue. 03, p. 423.
    Gilbert, N.D. 2004. HNN extensions of inverse semigroups and groupoids. Journal of Algebra, Vol. 272, Issue. 1, p. 27.
    Yamamura, Akihiro 2004. A class of inverse monoids acting on ordered forests. Journal of Algebra, Vol. 281, Issue. 1, p. 15.
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Locally full HNN extensions of inverse semigroups

  • Akihiro Yamamura (a1)
Abstract

We investigate a locally full HNN extension of an inverse semigroup. A normal form theorem is obtained and applied to the word problem. We construct a tree and show that a maximal subgroup of a locally full HNN extension acts on the tree without inversion. Bass-Serre theory is employed to obtain a group presentation of the maximal subgroup as a fundamental group of a certain graph of groups associated with the D-structure of the original semigroup.

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Copyright
COPYRIGHT: © Australian Mathematical Society 2001
References
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[2]Cherubini, A., Meakin, J. C. and Piochi, B., ‘Amalgams of free inverse semigroups’, Semigroup Forum 54 (1997), 199–220.
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[8]Jajcayova, T., HNN extensions of inverse semigroups (Ph.D. Thesis, University of Nebraska-Lincoln, 1997).
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[10]Lyndon, R. C. and Schupp, P. E., Combinatorial group theory (Springer, New York, 1976).
[11]Margolis, S. W. and Meakin, J. C., ‘Inverse monoids, trees and context-free languages’, Trans. Amer. Math. Soc. 335 (1993), 259–276.
[12]Meakin, J. C. and Yamamura, A., ‘Bass-Serre theory and inverse monoids’, in: Semigroups and Applications (eds. Howie, J. M. and Ruškuc, N.) (World Scientific, Singapore, 1998) pp. 125–140.
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[16]Yamamura, A., ‘HNN extensions of inverse semigroups and applications’, Int. J. Algebra Comput. (5) 7 (1997), 605–624.
[17]Yamamura, A., ‘HNN extensions of semilattices’, Int. J. Algebra Comput. (5) 9 (1999), 555–596.
[18]Yamamura, A., ‘Presentations of Bruck-Reilly extensions and decision problems’, Semigroup Forum (to appear).
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Journal of the Australian Mathematical Society
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  • EISSN: 1446-8107
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