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Abstract(s)
In this paper we consider the monoid OR(n) of all full transformations on a chain with n elements that preserve or reverse the orientation, as well as its submonoids OD(n) of all order-preserving or order-reversing elements, OP(n) of all orientation-preserving elements and O(n) of all order-preserving elements. By making use of some well known presentations, we show that each of these four monoids is a quotient of a bilateral semidirectproduct of two of its remarkable submonoids.
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Keywords
Bilateral Semidirect Products Transformation Semigroups Free Monoids Presentations Preserving Mappings Semigroups Presentations Endomorphism Chain
Citation
FERNANDES, Vítor H.; QUINTEIRO, Teresa M. - Bilateral semidirect product decompositions of transformation monoids. Semigroup Forum. ISSN 0037-1912. Vol. 82, n.º 2 (2011) p. 271-287.