On the ranks of semigroups of transformations on a finite set with restricted range
VH Fernandes, J Sanwong - Algebra Colloquium, 2014 - World Scientific
VH Fernandes, J Sanwong
Algebra Colloquium, 2014•World ScientificLet be the semigroup of all partial transformations on X, and be the subsemigroups of of all
full transformations on X and of all injective partial transformations on X, respectively. Given
a non-empty subset Y of X, let, and. In 2008, Sanwong and Sommanee described the largest
regular subsemigroup and determined Green's relations of. In this paper, we present
analogous results for both and. For a finite set X with| X|≥ 3, the ranks of, and are well
known to be 4, 3 and 3, respectively. In this paper, we also compute the ranks of, and for any …
full transformations on X and of all injective partial transformations on X, respectively. Given
a non-empty subset Y of X, let, and. In 2008, Sanwong and Sommanee described the largest
regular subsemigroup and determined Green's relations of. In this paper, we present
analogous results for both and. For a finite set X with| X|≥ 3, the ranks of, and are well
known to be 4, 3 and 3, respectively. In this paper, we also compute the ranks of, and for any …
Let be the semigroup of all partial transformations on X, and be the subsemigroups of of all full transformations on X and of all injective partial transformations on X, respectively. Given a non-empty subset Y of X, let , and . In 2008, Sanwong and Sommanee described the largest regular subsemigroup and determined Green's relations of . In this paper, we present analogous results for both and . For a finite set X with |X| ≥ 3, the ranks of , and are well known to be 4, 3 and 3, respectively. In this paper, we also compute the ranks of , and for any proper non-empty subset Y of X.
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