# Boolean matrices ... neither Boolean nor matrices

Discussiones Mathematicae - General Algebra and Applications (2000)

- Volume: 20, Issue: 1, page 141-151
- ISSN: 1509-9415

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topGabriele Ricci. "Boolean matrices ... neither Boolean nor matrices." Discussiones Mathematicae - General Algebra and Applications 20.1 (2000): 141-151. <http://eudml.org/doc/287705>.

@article{GabrieleRicci2000,

abstract = {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.},

author = {Gabriele Ricci},

journal = {Discussiones Mathematicae - General Algebra and Applications},

keywords = {universal matrix; functional application; generalized matrix; analytic monoid; Boolean matrices; incidence matrices of a graph},

language = {eng},

number = {1},

pages = {141-151},

title = {Boolean matrices ... neither Boolean nor matrices},

url = {http://eudml.org/doc/287705},

volume = {20},

year = {2000},

}

TY - JOUR

AU - Gabriele Ricci

TI - Boolean matrices ... neither Boolean nor matrices

JO - Discussiones Mathematicae - General Algebra and Applications

PY - 2000

VL - 20

IS - 1

SP - 141

EP - 151

AB - 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.

LA - eng

KW - universal matrix; functional application; generalized matrix; analytic monoid; Boolean matrices; incidence matrices of a graph

UR - http://eudml.org/doc/287705

ER -

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