Systems of Inequalities Characterizing Ring Homomorphisms. (17th November 2016) - Fechner, Włodzimierz; Olbryś, Andrzej
Abstract : Assume that T : P → R and U : P → R are arbitrary mappings between two partially ordered rings P and R . We study a few systems of functional inequalities which characterize ring homomorphisms. For example, we prove that if T and U satisfy T ( f + g ) ≥ T ( f ) + T ( g ),     U ( f · g ) ≥ U ( f ) · U ( g ), for all f, g ∈ P and T ≥ U, then U = T and this mapping is a ring homomorphism. Moreover, we find two other systems for which we obtain analogous assertions.