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        On presentations of Bruck-Reilly extensions

        Author
        Carvalho, Catarina
        Attention
        2299/10177
        Abstract
        We first consider the class of monoids in which every left invertible element is also right invertible, and prove that if a monoid belonging to this class admits a finitely presented Bruck–Reilly extension then it is finitely generated. This allow us to obtain necessary and sufficient conditions for the Bruck–Reilly extensions of this class of monoids to be finitely presented. We then prove that thes D-classes of a Bruck–Reilly extension of a Clifford monoid are Bruck–Reilly extensions of groups. This yields another necessary and sufficient condition for these Bruck–Reilly extensions to be finitely generated and presented. Finally, we show that a Bruck–Reilly extension of a Clifford monoid is finitely presented as an inverse monoid if and only if it is finitely presented as a monoid, and that this property cannot be generalized to Bruck–Reilly extensions of arbitrary inverse monoids.
        Publication date
        2009
        Published in
        Communications in Algebra
        Published version
        https://doi.org/10.1080/00927870802625638
        Other links
        http://hdl.handle.net/2299/10177
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