Korean J. Math. Vol. 30 No. 1 (2022) pp.109-119
DOI: https://doi.org/10.11568/kjm.2022.30.1.109

r-notion of conjugacy in partial transformation semigroup

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Aftab Hussain Shah
Mohd Rafiq Parray


In this paper, we present a new definition of conjugacy that can be applied to an arbitrary semigroup and it does not reduce to the universal relation in semigroups with a zero. We compare the new notion of conjugacy with existing notions, characterize the conjugacy in subsemigroups of partial transformations through digraphs and restrictive partial homomorphisms.

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