Some classical theorems in state residuated lattices

Document Type : Research Paper


1 Department of Mathematics, Shahrekord Branch, Islamic Azad University, Shahrekord, Iran.

2 Department of Mathematics, Persian Gulf University, Bushehr, Iran.



This paper, by considering the notion of a state residuated lattice morphism in the class of state residuated lattices, investigates some classical theorems namely the going up and lying over theorems. Results show that each state residuated lattice morphism fulfills these theorems. Also, some properties about prime filters of residuated lattices are obtained which are given in the paper.


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