States on semi-divisible generalized residuated lattices reduce to states on MV-algebras

DOI10.1016/j.fss.2008.01.036zbMath1188.06009OpenAlexW2052933125MaRDI QIDQ835280

Esko Turunen, Janne Mertanen

Publication date: 28 August 2009

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

Full work available at URL: https://doi.org/10.1016/j.fss.2008.01.036

zbMATH Keywords

pseudo-MV-algebraRiečan statemaximal filtercomplemented elementgood generalized residuated latticesemi-divisibility

Mathematics Subject Classification ID

Logical foundations of quantum mechanics; quantum logic (quantum-theoretic aspects) (81P10) MV-algebras (06D35) Ordered semigroups and monoids (06F05) Probability measures on groups or semigroups, Fourier transforms, factorization (60B15)

Related Items (17)

Generalized Bosbach states. I ⋮ The radical of a perfect residuated structure ⋮ Relationships between generalized Bosbach states and \(L\)-filters on residuated lattices ⋮ Generalized Bosbach and Riečan states on nucleus-based-Glivenko residuated lattices ⋮ Relative negations in non-commutative fuzzy structures ⋮ On fuzzy filters of pseudo BL-algebras ⋮ Generalized Bosbach and Riečan states based on relative negations in residuated lattices ⋮ States on commutative basic algebras ⋮ States and internal states on semihoops ⋮ On states and state operators on certain basic algebras ⋮ The lattices of 𝔏-fuzzy state filters in state residuated lattices ⋮ State maps on semihoops ⋮ Algebraic study to generalized Bosbach states on residuated lattices ⋮ States, state operators and quasi-pseudo-MV algebras ⋮ States on finite monoidal t-norm based algebras ⋮ Hybrid generalized Bosbach and Rie c̆ an states on non-commutative residuated lattices ⋮ The existence of states based on Glivenko semihoops

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