Cite this article as:

Poplavskii V. B. On idempotents of algebra of Boolean matrices. Izv. Saratov Univ. (N. S.), Ser. Math. Mech. Inform., 2012, vol. 12, iss. 2, pp. 26-33. DOI: https://doi.org/10.18500/1816-9791-2012-12-2-26-33

Language:

Russian

Heading:

Mathematics

UDC:

512.554+512.643

On idempotents of algebra of Boolean matrices

Authors:

Poplavskii Vladislav Bronislavovich, Saratov State University 1, Saratov State University, Russia, 410012, Saratov, Astrahanskaya st., 83 , poplavskivb@mail.ru

Abstract:

The structure of idempotent matrices in partial semigroups of matrices of arbitrary sizes with elements from arbitrary Boolean algebra with conjunctive and disjunctive partial multiplications is investigated. The connection of solvability of the simplest matrix equations with some kind of idempotent matrices which are called “secondary idempotents” is shown. Also we show the connection of arbitrary idempotent matrices with secondary idempotents and investigate their properties.

Key words:

Boolean matrices, matrix equations, idempotents.

DOI:

https://doi.org/10.18500/1816-9791-2012-12-2-26-33

References

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