Commutative directoids with sectional involutions

• Autorzy: Ivan Chajda
• Języki publikacji: EN

Abstrakty

EN

The concept of a commutative directoid was introduced by J. Ježek and R. Quackenbush in 1990. We complete this algebra with involutions in its sections and show that it can be converted into a certain implication algebra. Asking several additional conditions, we show whether this directoid is sectionally complemented or whether the section is an NMV-algebra.

Słowa kluczowe

EN

commutative directoid; sectional involution; sectional complement; d-implication algebra; NMV-algebra

Kategorie tematyczne

• 03G25: Other algebras related to logic
• 06A12: Semilattices
• 03G10: Lattices and related structures
• 06A06: Partial order, general
• 06D35: MV-algebras

• Wydawca: Faculty of Mathematics, Computer Science and Econometrics, University of Zielona Góra
• Czasopismo: Discussiones Mathematicae - General Algebra and Applications
• Rocznik: 2007
• Tom: 27
• Numer: 1
• Strony: 49-58

Daty

wydano

2007

otrzymano

2006-02-22

poprawiono

2006-12-13

Twórcy

autor

Ivan Chajda

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

Bibliografia

• [1] I. Chajda and J. Kühr, A non-associative generalization of MV-algebras, Math. Slovaca, to appear.
• [2] J. Ježek and R. Quackenbush, Directoids: algebraic models of up-directed sets, Algebra Universalis 27 (1990), 49-69.

Identyfikatory

DOI

10.7151/dmgaa.1118