f-Algebra in Quotient Space

Based on the knowledge of f-algebra, the concept of quotient f-algebra is mainly discussed. The sufficient condition when the quotient space is quotient f-algebra is given, and the quotient f-algebra that makes the kernel of a Riesz homomorphism as the equivalence class is obtained. Moreover, some important algebraic properties, such as commutative, semiprime and unital are studied, and the relationship between an f-algebra and its quotient space with respect to these properties are discussed in details.