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Rickart residuated lattices

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Abstract

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 \({\mathfrak {A}}\), is Rickart iff any its coannulet is a direct summand of \({\mathfrak {A}}\) 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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Acknowledgements

I would like to give heartfelt thanks to the referees for their very careful reading of the paper and for their very valuable comments and suggestions which improved the paper.

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  1. Department of Mathematics, Persian Gulf University, Bushehr, 75169, Iran

    Saeed Rasouli

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  1. Saeed Rasouli
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Correspondence to Saeed Rasouli.

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Rasouli, S. Rickart residuated lattices. Soft Comput 25, 13823–13840 (2021). https://doi.org/10.1007/s00500-021-06227-w

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