Geodesic
Commutative directoids with sectional involutions
Discussiones Mathematicae. General Algebra and Applications, Tome 27 (2007) no. 1, pp. 49-58 Cet article a éte moissonné depuis la source Library of Science

Voir la notice de l'article

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.
Keywords: commutative directoid, sectional involution, sectional complement, d-implication algebra, NMV-algebra 
@article{DMGAA_2007_27_1_a2,
     author = {Chajda, Ivan},
     title = {Commutative directoids with sectional involutions},
     journal = {Discussiones Mathematicae. General Algebra and Applications},
     pages = {49--58},
     year = {2007},
     volume = {27},
     number = {1},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/DMGAA_2007_27_1_a2/}
}
TY  - JOUR
AU  - Chajda, Ivan
TI  - Commutative directoids with sectional involutions
JO  - Discussiones Mathematicae. General Algebra and Applications
PY  - 2007
SP  - 49
EP  - 58
VL  - 27
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/DMGAA_2007_27_1_a2/
LA  - en
ID  - DMGAA_2007_27_1_a2
ER  - 
%0 Journal Article
%A Chajda, Ivan
%T Commutative directoids with sectional involutions
%J Discussiones Mathematicae. General Algebra and Applications
%D 2007
%P 49-58
%V 27
%N 1
%U http://geodesic.mathdoc.fr/item/DMGAA_2007_27_1_a2/
%G en
%F DMGAA_2007_27_1_a2
Chajda, Ivan. Commutative directoids with sectional involutions. Discussiones Mathematicae. General Algebra and Applications, Tome 27 (2007) no. 1, pp. 49-58. http://geodesic.mathdoc.fr/item/DMGAA_2007_27_1_a2/

[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.