The prime state ideal theorem in state residuated lattices
Publish Year: 1402
نوع سند: مقاله ژورنالی
زبان: English
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JR_CGASAT-18-1_006
تاریخ نمایه سازی: 28 فروردین 1402
Abstract:
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.
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Authors
Francis Woumfo
Departement of Mathematics and Computer Science, Faculty of Sciences, University of Dschang, Dschang, Cameroon
Etienne Romuald Temgoua
Department of Mathematics, Ecole Normale Sup´erieure, de Yaound´e, University of Yaound´e ۱, P.O. Box ۴۷, Yaound´e, Cameroon.
Celestin Lele
Department of Mathematics and Computer Science, Faculty of Science, University of Dschang, Dschang, Cameroon