Boolean matrices, the incidence matrices of a graph, are known not to be the (universal) matrices of a Boolean algebra. Here, we also show that their usual composition cannot make them the matrices of any algebra. Yet, later on, we "show" that it can. This seeming paradox comes from the hidden intrusion of a widespread set-theoretical (mis) definition and notation and denies its harmlessness. A minor modification of this standard definition might fix it.
@article{bwmeta1.element.bwnjournal-article-doi-10_7151_dmgaa_1012,
author = {Gabriele Ricci},
title = {Boolean matrices ... neither Boolean nor matrices},
journal = {Discussiones Mathematicae - General Algebra and Applications},
volume = {20},
year = {2000},
pages = {141-151},
zbl = {0964.08003},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmgaa_1012}
}
Gabriele Ricci. Boolean matrices ... neither Boolean nor matrices. Discussiones Mathematicae - General Algebra and Applications, Tome 20 (2000) pp. 141-151. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmgaa_1012/
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