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Abstract
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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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