Homomorphism-homogeneous monounary algebras
Éva Jungábel, Dragan Mašulović · Mathematica Slovaca · 2013
Abstract In 2006, P. J. Cameron and J. Nešetřil introduced the following variant of homogeneity: we say that a structure is homomorphism-homogeneous if every homomorphism between finitely generated substructures of the structure extends to an endomorphism of the structure. In several recent papers homomorphism-homogeneous objects in some well-known classes of algebras have been investigated (e.g. lattices and semilattices), while finite homomorphism-homogeneous groups were described in 1979 under the name of finite quasiinjective groups. In this paper we characterize homomorphism-homogenous monounary algebras of arbitrary cardinalities.