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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Published: Mar 30, 2022
Keywords:
Conjugacy, rp-hom, digraphs
Mathematics Subject Classification:
20M07, 20M15, 20M20.

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Aftab Hussain Shah
Department of Mathematics, Central University of Kashmir, City Ganderbal, Kashmir.
Mohd Rafiq Parray
Department of Mathematics, Central University of Kashmir, City Ganderbal, Kashmir.

Abstract

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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