Prime, minimal prime and maximal ideals spaces in residuated lattices

DOI10.1016/j.fss.2020.04.009zbMath1464.03094OpenAlexW3019171134MaRDI QIDQ2035407

Dana Piciu

Publication date: 24 June 2021

Published in: Fuzzy Sets and Systems (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.fss.2020.04.009

zbMATH Keywords

topologymaximal idealidealprime idealminimal prime idealresiduated latticeDe Morgan residuated latticeMTL algebra

Mathematics Subject Classification ID

Logical aspects of lattices and related structures (03G10) Lattice ideals, congruence relations (06B10) MV-algebras (06D35) De Morgan algebras, ?ukasiewicz algebras (lattice-theoretic aspects) (06D30)

Related Items (6)

Ideal theory on EQ-algebras ⋮ Preservation of properties of residuated algebraic structure by structures for the partial fuzzy set theory ⋮ Relative annihilators in bounded commutative residuated lattices ⋮ \(\mathcal{L}\)-fuzzy annihilators in residuated lattices ⋮ Fuzzy prime ideal theorem in residuated lattices ⋮ On state ideals and state relative annihilators in De Morgan state residuated lattices

Cites Work

• Some types of filters in residuated lattices
• Topological characterization of certain classes of lattices
• Isomorphic sheaf representations of normal lattices
• Mathematics behind fuzzy logic
• Metamathematics of fuzzy logic
• The prime and maximal spectra and the reticulation of BL-algebras
• The variety generated by perfect BL-algebras: an algebraic approach in a fuzzy logic setting
• Algebraic foundations of many-valued reasoning
• MV-algebras derived from ideals in BL-algebras
• On ideals in De Morgen residuated lattices
• Normal lattices
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