TY - JOUR
ID - 103288
TI - The prime state ideal theorem in state residuated lattices
JO - Categories and General Algebraic Structures with Applications
JA - CGASA
LA - en
SN - 2345-5853
AU - Woumfo, Francis
AU - Temgoua, Etienne Romuald Alomo
AU - Lele, Celestin
AD - Departement of Mathematics and Computer Science, Faculty of Sciences, University of Dschang, Dschang, Cameroon
AD - Department of Mathematics, Ecole Normale Sup´erieure, de Yaound´e, University of Yaound´e 1, P.O. Box 47, Yaound´e, Cameroon.
AD - Department of Mathematics and Computer Science, Faculty of Science, University of Dschang, Dschang, Cameroon
Y1 - 2023
PY - 2023
VL - 18
IS - 1
SP - 131
EP - 153
KW - State ideal
KW - frame
KW - Residuated lattice
DO - 10.52547/cgasa.2023.103288
N2 - 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.
UR - https://cgasa.sbu.ac.ir/article_103288.html
L1 - https://cgasa.sbu.ac.ir/article_103288_7c80a9cedf8e1ba5002830b5d68d31cf.pdf
ER -