대한수학회지 (Journal of the Korean Mathematical Society)

  • 제44권1호
  • /
  • Pages.169-178
  • /
  • 2007
  • /
  • 0304-9914(pISSN)
  • /
  • 2234-3008(eISSN)
대한수학회 (Korean Mathematical Society)
권호 표지
DOI QR코드

DOI QR Code

IDEMPOTENT MATRIX PRESERVERS OVER BOOLEAN ALGEBRAS

  • Song, Seok-Zun (Department of Mathematics and Research Institute of Basic Science Cheju National University) ;
  • Kang, Kyung-Tae (Department of Mathematics and Research Institute of Basic Science Cheju National University) ;
  • Beasley Leroy B. (Department of Mathematics and Statistics Utah State University)
  • 발행 : 2007.01.31
PDF 다운로드
⟨ 이전 논문 다음 논문 ⟩

초록

We consider the set of $n{\times}n$ idempotent matrices and we characterize the linear operators that preserve idempotent matrices over Boolean algebras. We also obtain characterizations of linear operators that preserve idempotent matrices over a chain semiring, the nonnegative integers and the nonnegative reals.

키워드

참고문헌

  1. R. B. Bapat, S. K. Jain, and L. E. Snyder, Nonnegative idempotent matrices and minus partial order, Linear Algebra Appl. 261 (1997), 143-154 https://doi.org/10.1016/S0024-3795(96)00364-3
  2. L. B. Beasley and N. J. Pullman, Boolean-rank-preserving operators and Boolean-rank-1 spaces, Linear Algebra Appl. 59 (1984), 55-77 https://doi.org/10.1016/0024-3795(84)90158-7
  3. L. B. Beasley and N. J. Pullman, Linear operators preserving idempotent matrices over fields, Linear Algebra Appl. 146 (1991), 7-20 https://doi.org/10.1016/0024-3795(91)90016-P
  4. L. B. Beasley and N. J. Pullman, Linear operators strongly preserving idempotent matrices over semirings, Linear Algebra Appl. 160 (1992), 217-229 https://doi.org/10.1016/0024-3795(92)90448-J
  5. L. B. Beasley, S. Z. Song, and S. G. Lee, Linear operators that preserve zero-term rank of Boolean matrices, J. Korean Math. Soc. 36 (1999), no. 6, 1181-1190
  6. G. H. Chan, M. H. Lim, and K. K. Tan, Linear preservers on matrices, Linear Algebra Appl. 93 (1987), 67-80 https://doi.org/10.1016/S0024-3795(87)90312-0
  7. K. H. Kim, Boolean matrix theory and applications, Pure and Applied Mathematics, Vol. 70, Marcel Dekker, New York, 1982
  8. S. Kirkland and N. J. Pullman, Linear operators preserving invariants of non-binary Boolean matrices, Linear and Multilinear Algebra 33 (1993), no. 3-4, 295-300
  9. S. Z. Song, L. B. Beasley, G. S. Cheon, and Y. B. Jun, Rank and Perimeter preservers of Boolean rank-1 matrices, J. Korean Math. Soc. 41 (2004), no. 2, 397-406 https://doi.org/10.4134/JKMS.2004.41.2.397
  10. S. Z. Song and K. T. Kang, Types and enumeration of idempotent matrices, Far East J. Math. Sci. 3 (2001), no. 6, 1029-1042

피인용 문헌

  1. Idempotent matrices over antirings vol.431, pp.5-7, 2009, https://doi.org/10.1016/j.laa.2009.03.035
  2. On Decompositions of Matrices over Distributive Lattices vol.2014, 2014, https://doi.org/10.1155/2014/202075
  3. Idempotent elements determined matrix algebras vol.435, pp.11, 2011, https://doi.org/10.1016/j.laa.2011.05.002
  4. On linear operators strongly preserving invariants of Boolean matrices vol.62, pp.1, 2012, https://doi.org/10.1007/s10587-012-0004-y
  5. NONBIJECTIVE IDEMPOTENTS PRESERVERS OVER SEMIRINGS vol.47, pp.4, 2010, https://doi.org/10.4134/JKMS.2010.47.4.805
  6. The Invertible Linear Operator Preserving {1,2}-Inverses of Matrices over Semirings vol.05, pp.01, 2015, https://doi.org/10.12677/PM.2015.51002
  7. Onn×nmatrices over a finite distributive lattice vol.60, pp.2, 2012, https://doi.org/10.1080/03081087.2011.574626