• Korean Journal of Mathematics
• /
• v.30 no.1
• /
• pp.109-119
• /
• 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.