The Loomis-Sikorski Theorems And The Prime Boolean Filter Lattices Of IMTL Algebras

In this paper, we studied the relations between valuations and filters in some fuzzy logic algebras, such as MV-algebras,â…¡-algebras, G-algebras R₀ -algebras, etc. We established the Loomis-Sikorski theorems for these fuzzy logic algebras. On the operations about prime Boolean fitter of IMTL algebra M. Let (?)B(M) be the set of all prime Booleafitters of IMTL algebra M and (?) =(?)B(M)∪{φ} . The∨-operation,∧-operation, order - reversing involution correspondence and adjoin pair ((?),→) on (?) are defined。The conclusions that(?) defined as above is a quasi- boolean algebra and is also a resituated lattice are obtained.