The concept of annihilator ideals is introduced in C-algebras. Some properties of these annihilator ideals are studied and then proved that the class of all annihilator ideals forms a complete Boolean algebra. A set of equivalent conditions are obtained for every ideal of a C-algebra to become an annihilator ideal. Some properties of homomorphic images and inverse images of annihilators ideals of a C-algebra are studied.

The concept of weak implicative filters is introduced in BEalgebras. Some characterizations of weak implicative filters are derived in terms of filters of a BE-algebra. Fuzzification is applied to the class of weak implicative filters. Some properties of fuzzy weak implicative filters are studied with respect to fuzzy relations and homomorphisms. The notion of triangular normed fuzzy weak implicative filters is introduced in BEalgebras and their properties are studied.

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The concept of normal C-algebras is introduced. The class of all normal C-algebras is characterized in terms of minimal prime ideals. Direct products of normal C-algebras are studied. A congruence is introduced in terms of multiplicative sets and an equivalency between the normalities of C-algebras and the respective quotient algebras is observed.

The concepts of boosters and β-filters are introduced in an MS -algebra and the β-filters are characterized in terms of boosters. It is then proved that the lattice of β-filters is isomorphic to the ideal lattice of the lattice of boosters. A set of equivalent conditions are derived for the lattice of boosters to become a relatively complemented lattice.