The going-up and going-down theorems in residuated lattices
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.
KeywordsResiduated 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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The author declares that he has no conflict of interest.
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This article does not contain any studies with human participants or animals performed by any of the authors.
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