%0 Journal Article
%T The prime state ideal theorem in state residuated lattices
%J Categories and General Algebraic Structures with Applications
%I Shahid Beheshti University
%Z 2345-5853
%A Woumfo, Francis
%A Temgoua, Etienne Romuald Alomo
%A Lele, Celestin
%D 2023
%\ 02/01/2023
%V 18
%N 1
%P 131-153
%! The prime state ideal theorem in state residuated lattices
%K State ideal
%K frame
%K Residuated lattice
%R 10.52547/cgasa.2023.103288
%X The aim of this paper is to establish the prime state ideal theorem in state residuated lattices (SRLs). We study the state ideals lattice $\mathcal{SI}(L)$ of a state residuated lattice $(L, \varphi)$ and prove that it is a complete Brouwerian lattice in which the meet and the join of any two compact elements are compact (coherent frame). We characterize the notion of prime state ideals in SRLs. In addition, we establish the condition for which the lattice $\mathcal{SI}(L)$ is a Boolean algebra.
%U https://cgasa.sbu.ac.ir/article_103288_7c80a9cedf8e1ba5002830b5d68d31cf.pdf