Geodesic
Two constructions of De Morgan algebras and De Morgan quasirings
Discussiones Mathematicae. General Algebra and Applications, Tome 29 (2009) no. 2, pp. 169-180.

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

De Morgan quasirings are connected to De Morgan algebras in the same way as Boolean rings are connected to Boolean algebras. The aim of the paper is to establish a common axiom system for both De Morgan quasirings and De Morgan algebras and to show how an interval of a De Morgan algebra (or De Morgan quasiring) can be viewed as a De Morgan algebra (or De Morgan quasiring, respectively).
Keywords: De Morgan algebra, De Morgan quasiring, D-algebra, interval algebra, Boolean element 
@article{DMGAA_2009_29_2_a4,
     author = {Chajda, Ivan and Eigenthaler, G\"unther},
     title = {Two constructions of {De} {Morgan} algebras and {De} {Morgan} quasirings},
     journal = {Discussiones Mathematicae. General Algebra and Applications},
     pages = {169--180},
     publisher = {mathdoc},
     volume = {29},
     number = {2},
     year = {2009},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/DMGAA_2009_29_2_a4/}
}
TY  - JOUR
AU  - Chajda, Ivan
AU  - Eigenthaler, Günther
TI  - Two constructions of De Morgan algebras and De Morgan quasirings
JO  - Discussiones Mathematicae. General Algebra and Applications
PY  - 2009
SP  - 169
EP  - 180
VL  - 29
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/DMGAA_2009_29_2_a4/
LA  - en
ID  - DMGAA_2009_29_2_a4
ER  - 
%0 Journal Article
%A Chajda, Ivan
%A Eigenthaler, Günther
%T Two constructions of De Morgan algebras and De Morgan quasirings
%J Discussiones Mathematicae. General Algebra and Applications
%D 2009
%P 169-180
%V 29
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/DMGAA_2009_29_2_a4/
%G en
%F DMGAA_2009_29_2_a4
Chajda, Ivan; Eigenthaler, Günther. Two constructions of De Morgan algebras and De Morgan quasirings. Discussiones Mathematicae. General Algebra and Applications, Tome 29 (2009) no. 2, pp. 169-180. http://geodesic.mathdoc.fr/item/DMGAA_2009_29_2_a4/

[1] Birkhoff, G.: Lattice Theory (3rd ed.), Publ. Amer. Math. Soc., Providence, R. I., 1967.

[2] Chajda I., Eigenthaler, G.: A note on orthopseudorings and Boolean quasirings, Österr. Akad. Wiss. Math.-Natur. Kl., Sitzungsberichte Abt. II, 207] (1998), 83-94.

[3] Chajda, I., Eigenthaler, G.: De Morgan quasirings, Contributions to General Algebra 18] (2008), Proceedings of the Klagenfurt Conference 2007, Verlag J. Heyn, Klagenfurt, 17-21.

[4] Chajda, I., Kühr, J.: A note on interval MV-algebras, Math. Slovaca 56] (2006), 47-52.

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

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

[7] Dorninger, D., Länger, H., Mączyński, M.: The logic induced by a system of homomorphisms and its various algebraic characterizations. Demonstratio Math. 30] (1977), 215-232.

[8] Dorninger, D., Länger, H., Mączyński, M.: Lattice properties of ring-like quantum logics, Intern. J. Theor. Phys. 39] (2000), 1015-1026.

[9] Droste, M., Kuich, W., Rahonis, G.: Multi-valued MSO logics over words and trees, Fundamenta Informaticae 84] (2008), 305-327.

[10] Dvurečenskij, A., Hyčko, M.: Algebras on subintervals of BL-algebras, pseudo-BL-algebras and bounded residuated Rl-monoids, Math. Slovaca 56] (2006), 135-144.