Simple, local and subdirectly irreducible state residuated lattices, By Saeed Rasoli

Research

Title	Simple, local and subdirectly irreducible state residuated lattices
Type	Article
Keywords	residuated lattice; state residuated lattice; state filter; simple state residuated lattice; local state residuated lattice; subdirectly irreducible state residuated lattice.
Journal	Revista de la Union Matematica Argentina
DOI	https://doi.org/10.33044/revuma.1722
Researchers	Mohammad Taheri (First researcher) , Farhad Khaksar Haghani (Second researcher) , Saeed Rasoli (Third researcher)

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.