Given a non-trivial automorphism (resp. anti-automorphism) of a semigroup, we study its homomorphic (resp. anti-homomorphic) extensions to a larger semigroup by considering the images of the absorbing elements. Then we exhibit some examples to show the application of the results obtained.
"A note on the extensions of the inversion map to the absorbing elements of a semigroup." Nihonkai Math. J. 26 (2) 127 - 134, 2015.