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n-Normal residuated lattices

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Abstract

The notion of n-normal residuated lattice, as a subclass of residuated lattices in which every prime filter contains at most n minimal prime filters, is introduced and investigated. Before that, the notion of \(\omega \)-filter is introduced and it is observed that the set of \(\omega \)-filters in a residuated lattice forms a distributive lattice on its own, which includes the set of coannulets as a sublattice. The class of n-normal residuated lattices is characterized in terms of their prime filters, minimal prime filters, coannulets and \(\omega \)-filters. It is shown that a residuated lattice is normal if and only if its reticulation is conormal. Finally, the existence of the greatest \(\omega \)-filters contained in a given filter of a normal residuated lattice is obtained.

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Acknowledgements

The authors are highly grateful to referees for their valuable comments and suggestions which were helpful in improving this paper.

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Authors and Affiliations

  1. Persian Gulf University, 75168, Bushehr, Iran

    Saeed Rasouli

  2. Department of Mathematics, School of System Design and Technology, Tokyo Denki University, Senju 5, Adachi, Tokyo, 120-8551, Japan

    Michiro Kondo

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  1. Saeed Rasouli
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  2. Michiro Kondo
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Correspondence to Saeed Rasouli.

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Communicated by A. Di Nola.

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Rasouli, S., Kondo, M. n-Normal residuated lattices. Soft Comput 24, 247–258 (2020). https://doi.org/10.1007/s00500-019-04346-z

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