Abstract
We develop the commutator theory for fuzzy congruence relations of general universal algebras. In particular, for algebras in modular varieties, we characterize the commutator of fuzzy congruences using the Day’s terms.
Highlights
The commutator is a binary operation on the lattice of normal subgroups of a group which has an important role in the study of solvable, Abelian and nilpotent groups
We have a binary operation in the lattice of normal subgroups
His work has laid the foundation for generalizing the commutator theory from groups and rings to an abstract operation on the lattice of congruences of an algebra in permutable varieties
Summary
The commutator is a binary operation on the lattice of normal subgroups of a group which has an important role in the study of solvable, Abelian and nilpotent groups. His work has laid the foundation for generalizing the commutator theory from groups and rings to an abstract operation on the lattice of congruences of an algebra in permutable varieties. This operation has the same useful properties that the commutator for groups (which is a special case of it) possesses. For each Θ, Φ, Θi ∈ FCon(A) and any surjective homomorphism π ∶ A → B, was not obtained in any form Taking this into account, in this paper, we consider a general universal algebra A of a fixed type F and define a binary operation, which we call it the commutator, on the lattice of fuzzy congruence relations on A having the above properties.
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