Geodesic
Varieties of Orthomodular Lattices. II
Canadian journal of mathematics, Tome 24 (1972) no. 2, pp. 328-337

Voir la notice de l'article provenant de la source Cambridge University Press

In this paper we continue the study of equationally defined classes of orthomodular lattices started in [1].The only atom in the lattice of varieties of orthomodular lattices is the variety of all Boolean algebras. Every nontrivial variety contains it. It follows from B. Jónsson [4, Corollary 3.2] that the variety [MO2] generated by the orthomodular lattice MO2 of Figure 1 covers the variety of all Boolean algebras. I t was first shown by R. J. Greechie (oral communication) and is not difficult to see that every variety not consisting of Boolean algebras only contains [MO2]. Again it follows from the result of Jónsson's mentioned above that the varieties generated by one of the orthomodular lattices of Figures 2 to 5 cover [MO2]. The Figures 4 and 5 are to be understood in such a way that the orthocomplement of every element is on the vertical line through this element. 
Bruns, Günter; Kalmbach, Gudrun. Varieties of Orthomodular Lattices. II. Canadian journal of mathematics, Tome 24 (1972) no. 2, pp. 328-337. doi: 10.4153/CJM-1972-027-4
@article{10_4153_CJM_1972_027_4,
     author = {Bruns, G\"unter and Kalmbach, Gudrun},
     title = {Varieties of {Orthomodular} {Lattices.} {II}},
     journal = {Canadian journal of mathematics},
     pages = {328--337},
     year = {1972},
     volume = {24},
     number = {2},
     doi = {10.4153/CJM-1972-027-4},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CJM-1972-027-4/}
}
TY  - JOUR
AU  - Bruns, Günter
AU  - Kalmbach, Gudrun
TI  - Varieties of Orthomodular Lattices. II
JO  - Canadian journal of mathematics
PY  - 1972
SP  - 328
EP  - 337
VL  - 24
IS  - 2
UR  - http://geodesic.mathdoc.fr/articles/10.4153/CJM-1972-027-4/
DO  - 10.4153/CJM-1972-027-4
ID  - 10_4153_CJM_1972_027_4
ER  - 
%0 Journal Article
%A Bruns, Günter
%A Kalmbach, Gudrun
%T Varieties of Orthomodular Lattices. II
%J Canadian journal of mathematics
%D 1972
%P 328-337
%V 24
%N 2
%U http://geodesic.mathdoc.fr/articles/10.4153/CJM-1972-027-4/
%R 10.4153/CJM-1972-027-4
%F 10_4153_CJM_1972_027_4

[1] 1. Bruns, G. and Kalmbach, G., Varieties of orthomodular lattices, Can. J. Math. 23 (1971), 802–810. Google Scholar

[2] 2. Greechie, R. J., On the structure of orthomodular lattices satisfying the chain condition, J. Combinatorial Theory 4 (1968), 210–218. Google Scholar

[3] 3. Greechie, R. J., Orthomodular lattices admitting no states, J. Combinatorial Theory 10 (1971), 119–132. Google Scholar

[4] 4. Jónsson, B., Algebras whose congruence lattices are distributive, Math. Scand. 21 (1967), 110–121. Google Scholar

Cité par Sources :