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On State Ideals and State Relative Annihilators in De Morgan State Residuated Lattices

Author

Listed:
  • Francis Woumfo
  • Blaise Bleriot Koguep Njionou
  • Etienne Romuald Temgoua Alomo
  • Celestin Lele
  • Sergejs Solovjovs

Abstract

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 Sâ„ L of a DMSRL L,Ï„ is a coherent frame. Then, we characterize the DMSRL for which the lattice Sâ„ L 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.

Suggested Citation

  • Francis Woumfo & Blaise Bleriot Koguep Njionou & Etienne Romuald Temgoua Alomo & Celestin Lele & Sergejs Solovjovs, 2022. "On State Ideals and State Relative Annihilators in De Morgan State Residuated Lattices," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2022, pages 1-14, June.
    • Handle: RePEc:hin:jijmms:6213448
    DOI: 10.1155/2022/6213448
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