Simple, local and subdirectly irreducible state residuated lattices

Authors

  • Mohammad Taheri Department of Mathematics, Shahrekord Branch, Islamic Azad University, Shahrekord, Iran
  • Farhad Khaksar Haghani Department of Mathematics, Shahrekord Branch, Islamic Azad University, Shahrekord, Iran
  • Saeed Rasouli Department of Mathematics, Shahrekord Branch, Islamic Azad University, Shahrekord, Iran & Department of Mathematics, Persian Gulf University, Bushehr, Iran

DOI:

https://doi.org/10.33044/revuma.1722

Abstract

This paper is devoted to investigating the notions of simple, local and subdirectly irreducible state residuated lattices and some of their related properties. The filters generated by a subset in state residuated lattices are characterized and it is shown that the lattice of filters of a state residuated lattice forms a complete Heyting algebra. Maximal, prime and minimal prime filters of a state residuated lattice are investigated and it is shown that any filter of a state residuated lattice contains a minimal prime filter. Finally, the relevant notions are discussed and characterized.

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Published

2021-11-04

Issue

Vol. 62 No. 2 (2021)

Section

Article

License

Copyright (c) 2022 Mohammad Taheri, Farhad Khaksar Haghani, Saeed Rasouli

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