TITLE:
On the Strongly Hopfian Acts over Semigroups
AUTHORS:
Ksenya Anatolyevna Kolesnikova, Igor Borisovich Kozhukhov
KEYWORDS:
Act Over Semigroup, Act Over Group, Strongly Hopfian Act
JOURNAL NAME:
Applied Mathematics,
Vol.16 No.2,
February
19,
2025
ABSTRACT: We find the necessary and sufficient conditions on a coproduct of connected acts over a semigroup to be strongly hopfian. From this, we deduce the conditions of the strong hopfness for unitary acts over groups. Moreover, we prove that a finite coproduct of strongly hopfian acts over an arbitrary semigroup is strongly hopfian.