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Keywords
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residuated lattice, filter; stabilizer, Galois connection, complete lattice, pseudocomplemented lattice
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Abstract
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The paper is devoted to introduce the notions of some types of stabilizers in non-commutative
residuated lattices and to investigate their properties. We establish a connection between (contravariant)
Galois connection and stabilizers of a residuated lattices. If A is a residuated lattice and F be a filter of A,
we show that the set of all stabilizers relative to F of a same type forms a complete lattice. Furthermore, we
prove that ST − F, ST − Fl and ST − Fs are pseudocomplemented lattices.
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