On duality of submodule lattices
Discussiones Mathematicae. General Algebra and Applications, Tome 20 (2000) no. 1, pp. 43-49.

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

An elementary proof is given for Hutchinson's duality theorem, which states that if a lattice identity λ holds in all submodule lattices of modules over a ring R with unit element then so does the dual of λ.
Keywords: submodule lattice, lattice identity, duality
@article{DMGAA_2000_20_1_a3,
     author = {Cz\'edli, G\'abor and Tak\'ach, G\'eza},
     title = {On duality of submodule lattices},
     journal = {Discussiones Mathematicae. General Algebra and Applications},
     pages = {43--49},
     publisher = {mathdoc},
     volume = {20},
     number = {1},
     year = {2000},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/DMGAA_2000_20_1_a3/}
}
TY  - JOUR
AU  - Czédli, Gábor
AU  - Takách, Géza
TI  - On duality of submodule lattices
JO  - Discussiones Mathematicae. General Algebra and Applications
PY  - 2000
SP  - 43
EP  - 49
VL  - 20
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/DMGAA_2000_20_1_a3/
LA  - en
ID  - DMGAA_2000_20_1_a3
ER  - 
%0 Journal Article
%A Czédli, Gábor
%A Takách, Géza
%T On duality of submodule lattices
%J Discussiones Mathematicae. General Algebra and Applications
%D 2000
%P 43-49
%V 20
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/DMGAA_2000_20_1_a3/
%G en
%F DMGAA_2000_20_1_a3
Czédli, Gábor; Takách, Géza. On duality of submodule lattices. Discussiones Mathematicae. General Algebra and Applications, Tome 20 (2000) no. 1, pp. 43-49. http://geodesic.mathdoc.fr/item/DMGAA_2000_20_1_a3/

[1] G. Frobenius, Theorie der linearen Formen mit ganzen Coefficienten, J. Reine Angew. Math. 86 (1879), 146-208.

[2] G. Hutchinson, On classes of lattices representable by modules, Proceedings of the University of Houston Lattice Theory Conference, Univ. Houston 1973, 69-94.

[3] G. Hutchinson and G. Czédli, A test for identities satisfied in submodule lattices, Algebra Universalis 8 (1978), 269-309.

[4] A.F. Pixley, Local Mal'cev conditions, Canadian Math. Bull. 15 (1972), 559-568.

[5] R. Wille, Kongruenzklassengeometrien, Lecture Notes in Math, no. 113, Springer-Verlag, Berlin-Heidelberg-New York 1970.