Systems of Inequalities Characterizing Ring Homomorphisms. (17th November 2016)

• Record Type: Journal Article
• Authors: Fechner, Włodzimierz; Olbryś, Andrzej
• Other Names: Wu Shanhe Academic Editor.
• Is Part Of: Journal of function spaces. Volume 2016(2016)
• Publication Date: 2016-11-17
• Subjects: Function spaces -- Periodicals; 515.7305
• DOI: 10.1155/2016/8069104
• Languages: English
• ISSNs: 2314-8896

Abstract

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.