# Generalized stone residuated lattices

Document Type : Research Paper

Author

Department of Mathematics, College of science, Persian Gulf University, Bushehr, 7516913817, Iran

10.29252/as.2020.1885

Abstract

This paper introduces and investigates the notion of a generalized Stone residuated lattice. It is observed that a residuated lattice is generalized Stone if and only if it is quasicomplemented and normal. Also, it is proved that a finite residuated lattice is generalized Stone if and only if it is normal. A characterization for generalized Stone residuated lattices is given by means of the new notion of $\alpha$-filters. Finally, it is shown that each non-unit element of a directly indecomposable generalized Stone residuated lattice is a dense element.

Keywords

#### References

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