Unary FA-presentable semigroups
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Automatic presentations, also called FA-presentations, were introduced to extend nite model theory to innite structures whilst retaining the solubility of interesting decision problems. A particular focus of research has been the classication of those structures of some species that admit automatic presentations. Whilst some successes have been obtained, this appears to be a dicult problem in general. A restricted problem, also of signicant interest, is to ask this question for unary automatic presentations: auto-matic presentations over a one-letter alphabet. This paper studies unary FA-presentable semigroups. We prove the following: Every unary FA-presentable structure admits an injective unary automatic presentation where the language of representatives consists of every word over a one-letter alphabet. Unary FA-presentable semigroups are locally nite, but non-nitely generated unary FA-presentable semigroups may be innite. Every unary FA-presentable semigroup satises some Burnside identity.We describe the Green's relations in unary FA-presentable semigroups. We investigate the relationship between the class of unary FA-presentable semigroups and various semigroup constructions. A classication is given of the unary FA-presentable completely simple semigroups.
Cain , A J , Ruskuc , N & Thomas , R M 2012 , ' Unary FA-presentable semigroups ' International Journal of Algebra and Computation , vol 22 , no. 4 , 1250038 . DOI: 10.1142/S0218196712500385
International Journal of Algebra and Computation
This is an author version of an article published in International Journal of Algebra and Computation © 2012 copyright World Scientific Publishing Company http://www.worldscinet.com/ijac/ijac.shtml
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