Mathematics – Rings and Algebras
Scientific paper
2010-02-08
Linear Algebra Appl. 433-2 (2010), 483-490
Mathematics
Rings and Algebras
12 pages, some minor corrections from the first version
Scientific paper
10.1016/j.laa.2010.03.021
Given an arbitrary field K, we reduce the determination of the singular
endomorphisms $f$ of M_n(K) that stabilize GL_n(K) to the classification of
n-dimensional division algebras over K. Our method, which is based upon
Dieudonn\'e's theorem on singular subspaces of M_n(K), also yields a proof for
the classical non-singular case.
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