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.
@article{bwmeta1.element.bwnjournal-article-doi-10_7151_dmgaa_1004,
author = {G\'abor Cz\'edli and G\'eza Tak\'ach},
title = {On duality of submodule lattices},
journal = {Discussiones Mathematicae - General Algebra and Applications},
volume = {20},
year = {2000},
pages = {43-49},
zbl = {0973.06008},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmgaa_1004}
}
Gábor Czédli; Géza Takách. On duality of submodule lattices. Discussiones Mathematicae - General Algebra and Applications, Tome 20 (2000) pp. 43-49. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmgaa_1004/
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