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Abstract(s)
In this article we consider the monoid O(mxn) of all order-preserving full transformations on a chain with mn elements that preserve a uniformm-partition and its submonoids O(mxn)(+) and O(mxn)(-) of all extensive transformations and of all co-extensive transformations, respectively. We determine their ranks and construct a bilateral semidirect product decomposition of O(mxn) in terms of O(mxn)(-) and O(mxn)(+).
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Keywords
Equivalence-Preserving Transformations Order-Preserving Transformations Semidirect Products Semigroups Mappings Endomorphims
Citation
FERNANDES, Vítor H.; QUINTEIRO, Teresa M. - On the monoids of transformations that preserve the order and a uniform partition. Communications in Algebra. ISSN 0092-7872. Vol. 39, n.º8 (2011) p. 2798-2815.