JP Journal of Algebra, Number Theory and Applications
Volume 3, Issue 3, Pages 405 - 413
(December 2003)
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ADDITIVE OPERATORS
PRESERVING RANK-ADDITIVITY ON TRIANGULAR MATRIX
ALGEBRA
Xiao-Min Tang (P. R. China) and Chong-Guang Cao (P. R. China)
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Abstract: We
characterize the additive operators preserving
rank-additivity on upper triangular matrix
algebras. Let Tn(F)
be the algebra of all n´n
upper triangular matrices over a field F,
then T is an additive bijective operator
preserving rank-additivity on Tn(F)
if and only if there exist invertible matrices U,
V ÎTn(F)
and a field isomorphism f
of F such that T(X)
= UXfV,
"X
= (xij) Î
Tn(F) or T(X)
= UYfV,
"X
= (xij) Î
Tn(F), where
Y
= (xn + 1– j, n+1–
i), Xf
= (f(xij)).
As applications, we determine the additive
bijective operators preserving rank-subtractivity
on Tn(F)
over the field F. |
Keywords and phrases: additive
operators, rank-additivity, rank-subtractivity. |
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