scholarly journals Residuated structures derived from commutative idempotent semirings

2019 ◽  
Vol 39 (1) ◽  
pp. 23
Author(s):  
Ivan Chajda ◽  
Helmut L¤nger
Keyword(s):  
Idempotent Semirings ◽  
Residuated Structures

scholarly journals Residuated Structures and Orthomodular Lattices

Studia Logica ◽  
2021 ◽  
Author(s):  
D. Fazio ◽  
A. Ledda ◽  
F. Paoli
Keyword(s):  
Algebraic Logic ◽  
Residuated Lattices ◽  
Quantum Structures ◽  
Heyting Algebras ◽  
Quantum Algebras ◽  
Orthomodular Lattices ◽  
Lattice Of Subvarieties ◽  
Residuated Structures ◽  
Common Framework ◽  
Mv Algebras

AbstractThe variety of (pointed) residuated lattices includes a vast proportion of the classes of algebras that are relevant for algebraic logic, e.g., $$\ell $$ ℓ -groups, Heyting algebras, MV-algebras, or De Morgan monoids. Among the outliers, one counts orthomodular lattices and other varieties of quantum algebras. We suggest a common framework—pointed left-residuated $$\ell $$ ℓ -groupoids—where residuated structures and quantum structures can all be accommodated. We investigate the lattice of subvarieties of pointed left-residuated $$\ell $$ ℓ -groupoids, their ideals, and develop a theory of left nuclei. Finally, we extend some parts of the theory of join-completions of residuated $$\ell $$ ℓ -groupoids to the left-residuated case, giving a new proof of MacLaren’s theorem for orthomodular lattices.

Semiconic idempotent residuated structures

2009 ◽  
Vol 61 (3-4) ◽  
pp. 413-430 ◽  
Author(s):  
Ai-ni Hsieh ◽  
James G. Raftery
Keyword(s):  
Residuated Structures

Residuated Structures, Concentric Sums and Finiteness Conditions

2008 ◽  
Vol 36 (10) ◽  
pp. 3632-3670 ◽  
Author(s):  
J. S. Olson ◽  
J. G. Raftery
Keyword(s):  
Finiteness Conditions ◽  
Residuated Structures

Idempotent semirings with a commutative additive reduct

2001 ◽  
Vol 64 (2) ◽  
pp. 289-296 ◽  
Author(s):  
Xianzhong Zhao
Keyword(s):  
Idempotent Semirings ◽  
Additive Reduct
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