• Korean Journal of Mathematics
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• 제30권1호
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• pp.109-119
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• 2022

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.