Distributivity of bounded lattices with sectionally antitone involutions

• Autorzy: Ivan Chajda
• Języki publikacji: EN

Abstrakty

EN

We present a simple condition under which a bounded lattice L with sectionally antitone involutions becomes an MV-algebra. In thiscase, L is distributive. However, we get a criterion characterizingdistributivity of L in terms of antitone involutions only.

Słowa kluczowe

EN

sectionally antitone involution; bounded lattice; distributive lattice; MV-algebra

Kategorie tematyczne

• 06F35: BCK-algebras, BCI-algebras
• 06A12: Semilattices
• 06D35: MV-algebras

• Wydawca: Faculty of Mathematics, Computer Science and Econometrics, University of Zielona Góra
• Czasopismo: Discussiones Mathematicae - General Algebra and Applications
• Rocznik: 2005
• Tom: 25
• Numer: 2
• Strony: 155-163

Daty

wydano

2005

otrzymano

2004-10-06

Twórcy

autor

Ivan Chajda

• Department of Algebra and Geometry, Palacký University of Olomouc, Tomkova 40, 779 00 Olomouc, Czech Republic

Bibliografia

• [1] J.C. Abbott, Semi-boolean algebra, Matem. Vestnik 4 (1967), 177-198.
• [2] R.L.O. Cignoli, I.M.L. D'Ottaviano and D. Mundici, Algebraic Foundations of Many-valued Reasoning, Kluwer, Dordrecht/Boston/London 2000.
• [3] I. Chajda, Lattices and semilattices having an antitone involution inevery upper interval, Comment. Math. Univ. Carol (CMUC) 44 (4) (2003), 577-585.
• [4] I. Chajda and P. Emanovský, Bounded lattices with antitone involutions and properties of MV-algebras, Discuss. Math. General Algebra and Appl. 24 (2004), 31-42.
• [5] I. Chajda, R. Halas and J. Kühr, Distributive lattices with sectionally antitone involutions, Acta Sci. Math. (Szeged), to appear.

Identyfikatory

DOI

10.7151/dmgaa.1098