Filters of R0-algebras

Abstract

The notion of fated filters in R0-algebras is introduced. Characterizations of (fated) filters are given. A filter generated by a set is established. By introducing the notion of finite ⊙-property, we show that if F is a nonempty subset of an R0-algebra L that has the finite ⊙-property, then there exists a maximal filter of L containing F.