FUNDAMENTALNAYA
I PRIKLADNAYA MATEMATIKA

(FUNDAMENTAL AND APPLIED MATHEMATICS)

2011/2012, VOLUME 17, NUMBER 4, PAGES 181-192

**On applications of associativity of dual compositions in the algebra
of Boolean matrices**

V. B. Poplavski

Abstract

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We consider matrices of arbitrary size with elements from an
arbitrary Boolean algebra with two partial multiplications that are
defined in a dual way and are not associative with respect to
each other in the general case.
We show the connection of solvability of the simplest matrix
equations, the matrix regularity, and the belonging to one-sided
principal ideals with associativity of some dual compositions.

Location: http://mech.math.msu.su/~fpm/eng/k1112/k114/k11411h.htm

Last modified: July 2, 2012