Mv-like algebras associated to lambda-ortholattices

• Autorzy: Chajda I. , Emanovsky P. , Kolarik M.
• Języki publikacji: EN

Abstrakty

EN

The concept of a ambda-lattice generalizes a lattice by substituting associativity by the so-called skew associativity. When a bounded ambda-lattice is equipped with a monotonous unary involution which is a complementation, it is called a ambda-ortholattice. For ambda-ortholattices a Sheffer operation is constructed and, moreover, a derived algebra analogous to an MV-algebra is assigned whenever the ambda-lattice has antitone involutions on sections.

Słowa kluczowe

EN

ortolattices; Sheffer operation; MV-algebra

PL

ortostruktury; proces Sheffera; algebra MV

• Wydawca: De Gruyter
• Czasopismo: Demonstratio Mathematica
• Rocznik: 2007
• Tom: Vol. 40, nr 2
• Strony: 261--270
• Opis fizyczny: Bibliogr. 6 poz.

Twórcy

autor

Chajda I.

autor

Emanovsky P.

autor

Kolarik M.

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

Bibliografia

• [1] G. Birkhoff, Lattice Theory, (3rd edition), Colloq. Publ. 25, Proc. Amer. Math. Soc., Providence, R. I., 1967.
• [2] I. Chajda, Sheffer operation in ortholattices, Acta Univ. Palack. Olomuc., Fac. Rerum. Natur. Math. 44 (2005), 19-23.
• [3] I. Chajda, H. Länger, Modifications of MV-algebras corresponding to strong ortholattices, Demonstratio Math. 38 (2005), 1-6.
• [4] J. Ježek, R. Quackenbush, Directoids: algebraic models of up-directed sets, Algebra Universalis 27 (1990), 49-69.
• [5] H. M. Sheffer, A set of five independent postulates for Boolean algebras, Trans. Amer. Math. Soc. 14 (1913), 481-488.
• [6] V. Snášel, ?-lattices, Math. Bohemica 122 (1997), 267-272.