Geodesic
Finite Projective Distributive Lattices
Canadian mathematical bulletin, Tome 13 (1970) no. 1, pp. 139-140

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

The theorem stated below is due to R. Balbes. The present proof is direct; it uses only the following two well-known facts: (i) Let K be a category of algebras, and let free algebras exist in K; then an algebra is projective if and only if it is a retract of a free algebra, (ii) Let F be a free distributive lattice with basis {x i | i ∊ I}; then ∧(x i | i ∊ J 0) ≤ ∨(x i | i ∊ J 1) implies J 0∩J 1≠φ. Note that (ii) implies (iii): If for J 0 ⊆ I, a, b ∊ F, ∧(x i | i ∊ J 0)≤a ∨ b, then ∧ (x i | i ∊ J 0)≤ a or b. 
Grätzer, G.; Wolk, B. Finite Projective Distributive Lattices. Canadian mathematical bulletin, Tome 13 (1970) no. 1, pp. 139-140. doi: 10.4153/CMB-1970-030-0
@article{10_4153_CMB_1970_030_0,
     author = {Gr\"atzer, G. and Wolk, B.},
     title = {Finite {Projective} {Distributive} {Lattices}},
     journal = {Canadian mathematical bulletin},
     pages = {139--140},
     year = {1970},
     volume = {13},
     number = {1},
     doi = {10.4153/CMB-1970-030-0},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1970-030-0/}
}
TY  - JOUR
AU  - Grätzer, G.
AU  - Wolk, B.
TI  - Finite Projective Distributive Lattices
JO  - Canadian mathematical bulletin
PY  - 1970
SP  - 139
EP  - 140
VL  - 13
IS  - 1
UR  - http://geodesic.mathdoc.fr/articles/10.4153/CMB-1970-030-0/
DO  - 10.4153/CMB-1970-030-0
ID  - 10_4153_CMB_1970_030_0
ER  - 
%0 Journal Article
%A Grätzer, G.
%A Wolk, B.
%T Finite Projective Distributive Lattices
%J Canadian mathematical bulletin
%D 1970
%P 139-140
%V 13
%N 1
%U http://geodesic.mathdoc.fr/articles/10.4153/CMB-1970-030-0/
%R 10.4153/CMB-1970-030-0
%F 10_4153_CMB_1970_030_0

[(2)] (2) Pacific J. Math. 21 (1967), 405-420.

[(3)] (3) The map φ is by necessity the same as in R. Balbes, loc. cit.

Cité par Sources :