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Discussiones Mathematicae General Algebra and Applications 20(1) (2000) 141-151
DOI: https://doi.org/10.7151/dmgaa.1012

BOOLEAN MATRICES ... NEITHER BOOLEAN NOR MATRICES

Gabriele Ricci

Universitá di Parma, I-43100 Parma, Italy
e-mail: ricci@prmat.math.unipr.it

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.

Keywords: universal matrix, functional application, generalized matrix, analytic monoid.

1991 Mathematics Subject Classification: Primary 08A02; Secondary 04A05, O8A35.

References

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Received 12 April 1999
Revised 24 November 1999
Revised 25 March 2000