Abstract
In this paper, we introduce some stabilizers and study related properties of them in residuated lattices. Then, we investigate the image and inverse image of a right and left stabilizer of a nonempty subset under a homomorphism. Besides, we discuss the relations between stabilizers and several special filters (ideals) in residuated lattices. Moreover, we also characterize some special classes of residuated lattices, for example, Heyting algebras and linearly ordered Heyting algebras, in terms of these stabilizers. Finally, we discuss the relations between these stabilizers and get that the right implicative stabilizers and right multiplicative stabilizers are order isomorphic.
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