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.
Woumfo,F , Temgoua,E R Alomo and Lele,C . (2023). The prime state ideal theorem in state residuated lattices. Categories and General Algebraic Structures with Applications, 18(1), 131-153. doi: 10.52547/cgasa.2023.103288
MLA
Woumfo,F , , Temgoua,E R Alomo, and Lele,C . "The prime state ideal theorem in state residuated lattices", Categories and General Algebraic Structures with Applications, 18, 1, 2023, 131-153. doi: 10.52547/cgasa.2023.103288
HARVARD
Woumfo F, Temgoua E R Alomo, Lele C. (2023). 'The prime state ideal theorem in state residuated lattices', Categories and General Algebraic Structures with Applications, 18(1), pp. 131-153. doi: 10.52547/cgasa.2023.103288
CHICAGO
F Woumfo, E R Alomo Temgoua and C Lele, "The prime state ideal theorem in state residuated lattices," Categories and General Algebraic Structures with Applications, 18 1 (2023): 131-153, doi: 10.52547/cgasa.2023.103288
VANCOUVER
Woumfo F, Temgoua E R Alomo, Lele C. The prime state ideal theorem in state residuated lattices. CGASA. 2023;18(1):131-153. doi: 10.52547/cgasa.2023.103288
