Izvestiya of Saratov University.

Mathematics. Mechanics. Informatics

ISSN 1816-9791 (Print)
ISSN 2541-9005 (Online)


For citation:

Poplavskii V. B. On Determinant Zeros of Boolean Matrices. Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, 2009, vol. 9, iss. 3, pp. 56-61. DOI: 10.18500/1816-9791-2009-9-3-56-61

This is an open access article distributed under the terms of Creative Commons Attribution 4.0 International License (CC-BY 4.0).
Published online: 
31.08.2009
Full text:
(downloads: 218)
Language: 
Russian
Heading: 
UDC: 
512.643.2+512.558

On Determinant Zeros of Boolean Matrices

Autors: 
Poplavskii Vladislav Bronislavovich, Saratov State University
Abstract: 

The properties of exteriority and interiority of square matrices with elements from arbitrary Boolean algebra are studied in this paper. The exteriorandinte riorparts formade generatepart of a matrix with zerodeterminant. Itisshown, inparticular, that the setof exteriorparts is a normal setinthe Boolean algebraofall Booleans quarematrices 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.

References: 
  1. Поплавский В.Б. О разложении определителей булевых матриц // Фундаментальная и прикладная математика. 2007. Т. 13, № 4. С. 199–223.
  2. Поплавский В.Б. Объемы и определители степеней транзитивных и рефлексивных булевых отношений на конечных множествах // Изв. Тульск. госун-та. Сер. Математика. Механика. Информатика. 2004. Т. 10, вып. 1. С. 134–141.
  3. Поплавский В.Б. О рангах, классах Грина и теории определителей булевых матриц // Дискрет. мат. 2008. Т. 20, № 4. С. 42–60.
  4. Сачков В.Н. Введение в комбинаторные методы дискретной математики. М.: Наука, 1982.
  5. Минк Х. Перманенты. М.: Мир, 1982.
  6. Владимиров Д.А. Булевы алгебры. М.: Наука, 1969.
  7. Golan J.S. Semirings and their Applications. Dordrecht: Kluwer Academic Publishers, 1999.
  8. Reutenauer C., Straubing H. Inversion of matrices over a commutative semiring // J. of Algebra. 1984. № 88. С. 350–360.