대한수학회보 (Bulletin of the Korean Mathematical Society)

  • 제54권1호
  • /
  • Pages.277-287
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  • 2017
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  • 1015-8634(pISSN)
  • /
  • 2234-3016(eISSN)
대한수학회 (Korean Mathematical Society)
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INJECTIVE LINEAR MAPS ON τ∞(F) THAT PRESERVE THE ADDITIVITY OF RANK

  • Slowik, Roksana (Institute of Mathematics Silesian University of Technology)
  • 투고 : 2016.02.01
  • 발행 : 2017.01.31
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초록

We consider ${\tau}_{\infty}(F)$ - the space of upper triangular infinite matrices over a field F. We investigate injective linear maps on this space which preserve the additivity of rank, i.e., the maps ${\phi}$ such that rank(x + y) = rank(x) + rank(y) implies rank(${\phi}(x+y)$) = rank(${\phi}(x)$) + rank(${\phi}(y)$) for all $x,\;y{\in}{\tau}_{\infty}(F)$.

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참고문헌

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