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The going-up and going-down theorems in residuated lattices

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Abstract

This paper investigates the going-up, lying-over and going-down properties for residuated morphisms. The results show that each residuated morphism fulfills the going-up and lying-over properties. Some topological characterizations are obtained for them. Moreover, the MTL morphisms which fulfill the going-down property are characterized. During this research, some facts about prime and minimal prime filters of residuated lattices are also obtained which are given in the paper.

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Acknowledgements

The author is highly grateful to referees for their valuable comments and suggestions which were helpful in improving this 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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Communicated by A. Di Nola.

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Rasouli, S. The going-up and going-down theorems in residuated lattices. Soft Comput 23, 7621–7635 (2019). https://doi.org/10.1007/s00500-019-03780-3

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