Cao, Chong-Guang; Zhang, Xian Additive surjections preserving rank one and applications. (English) Zbl 1075.15007 Georgian Math. J. 11, No. 2, 209-217 (2004). The authors characterize epimorphisms of the additive group of the full matrix algebra \(M_n(F)\) over a field \(F\), preserving rank one. Every such epimorphism \(f\) is uniquely determined by two automorphisms of the vector space \(F^n\) and a field automorphism \(g\), i.e. there exist matrices \(P,Q\in\text{GL}_n(F)\) such that either \(f(A)= PA^gQ\) or \(f(A)= P(A^g)^T Q\), where \(A^g= (g(a_{ij}))\) for \(A= (a_{ij})\). Reviewer: Witold Wiȩsław (Wrocław) Cited in 5 Documents MSC: 15A04 Linear transformations, semilinear transformations 15A03 Vector spaces, linear dependence, rank, lineability 15A30 Algebraic systems of matrices 16S50 Endomorphism rings; matrix rings Keywords:rank one preserving epimorphisms; full matrix algebra PDFBibTeX XMLCite \textit{C.-G. Cao} and \textit{X. Zhang}, Georgian Math. J. 11, No. 2, 209--217 (2004; Zbl 1075.15007) Full Text: EuDML