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Keywords
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Rickart residuated lattice, Baer residuated lattice, Quasicomplemented residuated lattice, Normal residuated
lattice, Generalized stone residuated lattice
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Abstract
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In this paper, the notion of a Rickart residuated lattice is introduced and investigated. A residuated lattice is called Rickart
if any its coannulet is generated by a complemented element. It is observed that a residuated lattice A, is Rickart iff any its
coannulet is a direct summand of A iff it is quasicomplemented and normal iff it is generalized Stone. Some algebraic and
topological characterizations are obtained, and some facts about pure and Stone filters are also extracted, which are given in
the paper.
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