On state ideals and state relative annihilators in De Morgan state residuated lattices
type: Item
instance of: scholarly article
title: On state ideals and state relative annihilators in De Morgan state residuated lattices
zbMATH Open document ID: 1497.03068
DOI: 10.1155/2022/6213448
author: Francis Woumfo
author: Blaise Bleriot Koguep Njionou
author: Etienne Romuald Temgoua Alomo
author: C. Lele
published in: International Journal of Mathematics and Mathematical Sciences
publication date: 2022-09-30T00:00:00Z
review text: Summary: The concept of state has been considered in commutative and noncommutative logical systems, and their properties are at the center for the development of an algebraic investigation of probabilistic models for those algebras. This article mainly focuses on the study of the lattice of state ideals in De Morgan state residuated lattices (DMSRLs). First, we prove that the lattice of all state ideals \(\mathcal{SI}\left( L\right)\) of a DMSRL \(\left( L, \tau\right)\) is a coherent frame. Then, we characterize the DMSRL for which the lattice \(\mathcal{SI}\left( L\right)\) is a Boolean algebra. In addition, we bring in the concept of state relative annihilator of a given nonempty subset with respect to a state ideal in DMSRL and investigate various properties. We prove that state relative annihilators are a particular kind of state ideals. Finally, we investigate the notion of prime state ideal in DMSRL and establish the prime state ideal theorem.
Mathematics Subject Classification ID: 03G10
Mathematics Subject Classification ID: 03G25
zbMATH DE Number: 7595553
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2022/6213448
OpenAlex ID: W4283591922
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description: scientific article; zbMATH DE number 7595553