مشخصات پژوهش

The notions of coannihilator and coannulet in a residuated lattice are investigated. For a residuated lattice A, it is shown that γ(A), the set of coannulets of A, is a sublattice of Γ(A), the Boolean lattice of coannihilators of A. It is observed that γ(A) is a Boolean sublattice of Γ(A) if and only if A is quasicomplemented and γ(A) is a sublattice of F(A), the filter lattice of A, if and only if A is normal. Finally, it is shown that γ(A) is a Boolean sublattice of F(A) if and only if A is generalized Stone. During this research, some facts about coannihilators, coannulets and dual coannulets of a residuated lattice are also obtained which are given in the paper.