Title of article :
The prime state ideal theorem in state residuated lattices
Author/Authors :
Woumfo ، Francis Department of Mathematics and Computer Science - Faculty of Sciences - University of Dschang , Alomo ، Etienne Romuald Temgoua Department of Mathematics - University of Yaound´e 1 , Lele ، Celestin Department of Mathematics and Computer Science - Faculty of Science - University of Dschang
Abstract :
The aim of this paper is to establish the prime state ideal the-orem in state residuated lattices (SRLs). We study the state ideals lattice SI(L) of a state residuated lattice (L, φ) and prove that it is a complete Brouwerian lattice in which the meet and the join of any two compact ele- ments are compact (coherent frame). We characterize the notion of prime state ideals in SRLs. In addition, we establish the condition for which the lattice SI(L) is a Boolean algebra.
Keywords :
State ideal , frame , Residuated lattice
Journal title :
Categories and General Algebraic Structures with Applications
Journal title :
Categories and General Algebraic Structures with Applications
