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

  • Saeed RasouliEmail author


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.


Residuated lattice Going-up theorem Lying-over theorem Going-down theorem 



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

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Conflict of interest

The author declares that he has no conflict of interest.

Human and animal rights

This article does not contain any studies with human participants or animals performed by any of the authors.


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© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department of MathematicsPersian Gulf UniversityBushehrIran

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