(S, *) is a semigroup S equipped with a unary operation "*". This work is devoted to a class of unary semigroups, namely E- *-. A unary semigroup (S, *) is called an E-inversive *-semigroup if the following identities hold: , , . In this paper, E-inversive *-semigroups are characterized by several methods. Furthermore, congruences on these semigroups are also studied.
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