Geodesic
A common approach to directoids with an antitone involution and D-quasirings
Discussiones Mathematicae. General Algebra and Applications, Tome 28 (2008) no. 2, pp. 139-145.

Voir la notice de l'article provenant de la source Library of Science

We introduce the so-called DN-algebra whose axiomatic system is a common axiomatization of directoids with an antitone involution and the so-called D-quasiring. It generalizes the concept of Newman algebras (introduced by H. Dobbertin) for a common axiomatization of Boolean algebras and Boolean rings.
Keywords: directoid, antitone involution, D-quasiring, DN-algebra, a-mutation 
@article{DMGAA_2008_28_2_a0,
     author = {Chajda, Ivan and Kola\v{r}{\'\i}k, Miroslav},
     title = {A common approach to directoids with an antitone involution and {D-quasirings}},
     journal = {Discussiones Mathematicae. General Algebra and Applications},
     pages = {139--145},
     publisher = {mathdoc},
     volume = {28},
     number = {2},
     year = {2008},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/DMGAA_2008_28_2_a0/}
}
TY  - JOUR
AU  - Chajda, Ivan
AU  - Kolařík, Miroslav
TI  - A common approach to directoids with an antitone involution and D-quasirings
JO  - Discussiones Mathematicae. General Algebra and Applications
PY  - 2008
SP  - 139
EP  - 145
VL  - 28
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/DMGAA_2008_28_2_a0/
LA  - en
ID  - DMGAA_2008_28_2_a0
ER  - 
%0 Journal Article
%A Chajda, Ivan
%A Kolařík, Miroslav
%T A common approach to directoids with an antitone involution and D-quasirings
%J Discussiones Mathematicae. General Algebra and Applications
%D 2008
%P 139-145
%V 28
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/DMGAA_2008_28_2_a0/
%G en
%F DMGAA_2008_28_2_a0
Chajda, Ivan; Kolařík, Miroslav. A common approach to directoids with an antitone involution and D-quasirings. Discussiones Mathematicae. General Algebra and Applications, Tome 28 (2008) no. 2, pp. 139-145. http://geodesic.mathdoc.fr/item/DMGAA_2008_28_2_a0/

[1] G. Birkhoff, Lattice Theory, (3rd edition), Colloq. Publ. 25, Proc. Amer. Math. Soc., Providence, R. I., 1967.

[2] I. Chajda and M. Kolařík, Directoids with an antitone involution, Comment. Math. Univ. Carolinae (CMUC) 48 (2007), 555-567.

[3] I. Chajda and H. Länger, A common generalization of ortholattices and Boolean quasirings, Demonstratio Math. 15 (2007), 769-774.

[4] H. Dobbertin, Note on associative Newman algebras, Algebra Universalis 9 (1979), 396-397.

[5] D. Dorninger, H. Länger andM. Mączyński, The logic induced by a system of homomorphisms and its various algebraic characterizations, Demonstratio Math. 30 (1997), 215-232.

[6] J. Ježek and R. Quackenbush, Directoids: algebraic models of up-directed sets, Algebra Universalis 27 (1990), 49-69.