대한수학회지 (Journal of the Korean Mathematical Society)

  • 제47권4호
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  • Pages.805-818
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  • 2010
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  • 0304-9914(pISSN)
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  • 2234-3008(eISSN)
대한수학회 (Korean Mathematical Society)
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NONBIJECTIVE IDEMPOTENTS PRESERVERS OVER SEMIRINGS

  • 투고 : 2008.10.01
  • 발행 : 2010.07.01
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초록

We classify linear maps which preserve idempotents on $n{\times}n$ matrices over some classes of semirings. Our results include many known semirings like the semiring of all nonnegative integers, the semiring of all nonnegative reals, any unital commutative ring, which is zero divisor free and of characteristic not two (not necessarily a principal ideal domain), and the ring of integers modulo m, where m is a product of distinct odd primes.

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참고문헌

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피인용 문헌

  1. Onn×nmatrices over a finite distributive lattice vol.60, pp.2, 2012, https://doi.org/10.1080/03081087.2011.574626
  2. Idempotent matrices over antirings vol.431, pp.5-7, 2009, https://doi.org/10.1016/j.laa.2009.03.035
  3. On linear operators strongly preserving invariants of Boolean matrices vol.62, pp.1, 2012, https://doi.org/10.1007/s10587-012-0004-y
  4. On Decompositions of Matrices over Distributive Lattices vol.2014, 2014, https://doi.org/10.1155/2014/202075
  5. 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