A note on bilateral semidirect product decompositions of some monoids of order-preserving partial permutations

Fernandes, Vítor Hugo; Quinteiro, Teresa

http://hdl.handle.net/10400.21/9710

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Authors

Fernandes, Vítor Hugo

Quinteiro, Teresa

Abstract(s)

In this note we consider the monoid PODIn of all monotone partial permutations on {1,....,n} and its submonoids DPn, POIn and ODPn of all partial isometries, of all order-preserving partial permutations and of all order-preserving partial isometries, respectively. We prove that both the monoids POIn and ODPn are quotients of bilateral semidirect products of two of their remarkable submonoids, namely of extensive and of co-extensive transformations. Moreover, we show that PODIn is a quotient of a semidirect product of POIn and the group C-2 of order two and, analogously, DPn is a quotient of a semidirect product of ODPn and C-2.

Keywords

Transformations Partial isometries Order-preserving Semidirect products Pseudovarieties

URI

http://hdl.handle.net/10400.21/9710

Citation

FERNANDES, Vítor Hugo; QUINTEIRO, Teresa M. – A note on bilateral semidirect product decompositions of some monoids of order-preserving partial permutations. Bulletin of the Korean Mathematical Society. ISSN 1015-8634. Vol. 53, N.º 2 (2016), pp. 495-506