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Abstract
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The paper is devoted to study the notions of right and left stabilizers in residuated lattices relative to a filter. We establish a connection between right and left stabilizers in residuated lattices relative to a filter and (contravariant) Galois connection. We define a new class of residuated lattices, called $\mathcal{RS-RL}$ and we show this class is a subquasivariety of the residuated lattices variety.
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