- Tytuł:
- Bounded lattices with antitone involutions and properties of MV-algebras
- Autorzy:
-
Chajda, Ivan
Emanovský, Peter - Powiązania:
- https://bibliotekanauki.pl/articles/728914.pdf
- Data publikacji:
- 2004
- Wydawca:
- Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
- Tematy:
-
antitone involution
distributive lattice
implication algebra
MV-algebra - Opis:
- We introduce a bounded lattice L = (L;∧,∨,0,1), where for each p ∈ L there exists an antitone involution on the interval [p,1]. We show that there exists a binary operation · on L such that L is term equivalent to an algebra A(L) = (L;·,0) (the assigned algebra to L) and we characterize A(L) by simple axioms similar to that of Abbott's implication algebra. We define new operations ⊕ and ¬ on A(L) which satisfy some of the axioms of MV-algebra. Finally we show what properties must be satisfied by L or A(L) to obtain all axioms of MV-algebra.
- Źródło:
-
Discussiones Mathematicae - General Algebra and Applications; 2004, 24, 1; 31-42
1509-9415 - Pojawia się w:
- Discussiones Mathematicae - General Algebra and Applications
- Dostawca treści:
- Biblioteka Nauki
Artykuł