\(\phi\)-orthogonally additive mappings. I (Q1187303)

One says that the elements \(x,y\in X\) of a vector space \(X\) over an Euclidean ordered field are \(\varphi\)-orthogonal if \(\varphi(x,y)=0\) for a non-isotropic bilinear form \(\varphi\). In the paper this concept is treated and is generalized for vector spaces over arbitrary fields, sesquilinear forms with respect to the automorphisms of the field and for orthogonally additive mappings with values in Abelian groups.