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Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, 2009, Volume 9, Issue 3, Pages 56–61
DOI: https://doi.org/10.18500/1816-9791-2009-9-3-56-61 (Mi isu61) 		 
Mathematics

On determinant zeros of boolean matrices

V. B. Poplavskii

Saratov State University, Chair of Geometry
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DOI: https://doi.org/10.18500/1816-9791-2009-9-3-56-61
Abstract: The properties of exteriority and interiority of square matrices with elements from arbitrary Boolean algebra are studied in this paper. The exterior and interior parts form a degenerate part of a matrix with zero determinant. It is shown, in particular, that the set of exterior parts is a normal set in the Boolean algebra of all Boolean square matrices and it is a lower semilattice. The set of interior parts is an upper semilattice. Moreover linear combinations and even polynomials of the interiorities also belong to it.
Key words: Boolean matrices, determinant, degenerate matrices.
Document Type: Article
UDC: 512.643.2+512.558
Language: Russian
Citation: V. B. Poplavskii, “On determinant zeros of boolean matrices”, Izv. Saratov Univ. Math. Mech. Inform., 9:3 (2009), 56–61
Citation in format AMSBIB
\Bibitem{Pop09}
\by V.~B.~Poplavskii
\paper On determinant zeros of boolean matrices
\jour Izv. Saratov Univ. Math. Mech. Inform.
\yr 2009
\vol 9
\issue 3
\pages 56--61
\mathnet{http://mi.mathnet.ru/isu61}
\crossref{https://doi.org/10.18500/1816-9791-2009-9-3-56-61}
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    		Известия Саратовского университета. Новая серия. Серия Математика. Механика. Информатика
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