Simple, local and subdirectly irreducible state residuated lattices

M. Taheri ^[1] ; F. Khaksar Haghani ^[1] ; S. Rasouli ^[1]
1. [1] Islamic Azad University
  
  Islamic Azad University
  
  Irán
Localización: Revista de la Unión Matemática Argentina, ISSN 0041-6932, ISSN-e 1669-9637, Vol. 62, Nº. 2, 2021, págs. 365-383
Idioma: inglés
DOI: 10.33044/revuma.1722
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Resumen
- 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.