The paper presents simple proofs of the Cauchy-Schwartz inequality and the negative discriminant property in archimedean almost f-algebras^[5], based on a sequence approximation.
Based on the knowledge off-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 ker...Based on the knowledge off-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.展开更多
文摘The paper presents simple proofs of the Cauchy-Schwartz inequality and the negative discriminant property in archimedean almost f-algebras^[5], based on a sequence approximation.
基金The Science Research Start-up Foundation for Young Teachers of Southwest Jiaotong University ( No.2008Q074)
文摘Based on the knowledge off-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.
