Multiplicative structure of biorthomorphisms and relation with orthomorphisms

In this study, the definitions of homomorphism, isomorphism and orthomorphism, which are the basis of biorthomorphism, have been made on Riesz spaces. As the study is carried out for Riesz spaces, basic informations about Riesz spaces and Riesz algebra are briefly explained. The structure of f-algebras and semiprime of biorthomorphisms defined on Archimedean Riesz spaces are investigated. The releationship between orthomorphisms and biorthomorphisms, the multiplicative structure of biorthomorphisms and their properties are examined. In particular, the embedding of the space of orthomorphisms into that of biorthomorphisms is investigated.