António José Mesquita da Cunha Machado Malheiro
(CAUL)
12/07/2005
International Conference on Semigroups and Languages in honour of the 65th birthday of Donald B. McAlister
On Finite Derivation Type and Subsemigroups
Let S be the semigroup defined by a presentation P = hA | Ri and let T
be the subsemigroup of S generated by X A+. In [1] the authors give a
general presentation Q for the subsemigroup T in terms of the generators X.
Although the obtained presentation is infinite it yields a method for finding
a finite presentation for T.
In general, associated to a presentation P we have a 2-complex D(P)
called the Squier complex. The semigroup defined by P is said to be of
finite derivation type if there is a finite trivializer of D(P). Now, given a
trivializer of D(P) we present a (infinite) trivializer of the Squier complex
associated to the presentation Q of the subsemigroup T generated by X. This
result is obtained by making use of the same rewriting techniques exhibited
in [1]. Also, similarly to the case in [1], this result provides a method to
find a finite trivializer of the Squier complex D(Q), in some special cases of
subsemigroups.
References
[1] C. M. Campbell, E.F. Robertson, N. Ruˇskuc, and R. M. Thomas.
Reidemeister-Schreier type rewriting for semigroups. Semigr. Forum,
51:47–62, 1995. |
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