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.
@article{bwmeta1.element.bwnjournal-article-doi-10_7151_dmgaa_1139,
author = {Ivan Chajda and Miroslav Kola\v r\'\i k},
title = {A common approach to directoids with an antitone involution and D-quasirings},
journal = {Discussiones Mathematicae - General Algebra and Applications},
volume = {28},
year = {2008},
pages = {139-145},
zbl = {1195.06002},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmgaa_1139}
}
Ivan Chajda; Miroslav Kolařík. A common approach to directoids with an antitone involution and D-quasirings. Discussiones Mathematicae - General Algebra and Applications, Tome 28 (2008) pp. 139-145. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmgaa_1139/
[000] [1] G. Birkhoff, Lattice Theory, (3rd edition), Colloq. Publ. 25, Proc. Amer. Math. Soc., Providence, R. I., 1967.
[001] [2] I. Chajda and M. Kolařík, Directoids with an antitone involution, Comment. Math. Univ. Carolinae (CMUC) 48 (2007), 555-567. | Zbl 1199.06012
[002] [3] I. Chajda and H. Länger, A common generalization of ortholattices and Boolean quasirings, Demonstratio Math. 15 (2007), 769-774. | Zbl 1160.08003
[003] [4] H. Dobbertin, Note on associative Newman algebras, Algebra Universalis 9 (1979), 396-397. | Zbl 0445.06010
[004] [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. | Zbl 0879.06005
[005] [6] J. Ježek and R. Quackenbush, Directoids: algebraic models of up-directed sets, Algebra Universalis 27 (1990), 49-69. | Zbl 0699.08002