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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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  • Currently known as: Journal of the Australian Mathematical Society Title history
    Journal of the Australian Mathematical Society, Volume 70, Issue 2
  • April 2001, pp. 235-272

Locally full HNN extensions of inverse semigroups

  • Akihiro Yamamura (a1)
  • DOI: http://dx.doi.org/10.1017/S1446788700002639
  • Published online: 01 April 2009
Abstract
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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[1]P. Bennett , ‘On the structure of inverse semigroup amalgams’, Int. J. Algebra Comput. (5) 7 (1997), 577604.

[2]A. Cherubini , J. C. Meakin and B. Piochi , ‘Amalgams of free inverse semigroups’, Semigroup Forum 54 (1997), 199220.

[4]S. Haataja , S. W. Margolis and J. C. Meakin , ‘On the structure of full regular semigroup amalgams’, J. Algebra 183 (1996), 3854.

[5]T. E. Hall , ‘Free products with amalgamation of inverse semigroups’, J. Algebra 34 (1975), 375385.

[6]T. E. Hall , ‘Amalgamation of inverse and regular semigroups’, Trans. Amer. Math. Soc. 246 (1978), 395406.

[7]J. M. Howie , ‘Embedding theorems for semigroups’, Quart. J. Math. 14 (1963), 254258.

[9]M. V. Lawson , Inverse semigroups (World Scientific, Singapore, 1998).

[11]S. W. Margolis and J. C. Meakin , ‘Inverse monoids, trees and context-free languages’, Trans. Amer. Math. Soc. 335 (1993), 259276.

[14]J.-P. Serre , Trees (Springer, New York, 1980).

[16]A. Yamamura , ‘HNN extensions of inverse semigroups and applications’, Int. J. Algebra Comput. (5) 7 (1997), 605624.

[17]A. Yamamura , ‘HNN extensions of semilattices’, Int. J. Algebra Comput. (5) 9 (1999), 555596.

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Journal of the Australian Mathematical Society
  • ISSN: 1446-7887
  • EISSN: 1446-8107
  • URL: /core/journals/journal-of-the-australian-mathematical-society
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