Maps preserving zeros of matrix polynomials

A. Guterman, B. Kuzma

Research output: Contribution to journalArticlepeer-review

2 Scopus citations


We study non-linear maps on the set of n × n matrices over a field, which preserve the zeros of a fixed homogeneous multilinear polynomial. This solves Kaplansky-Watkins problem from 1976 about the structure of such transformations.

Original languageEnglish
Pages (from-to)508-510
Number of pages3
JournalDoklady Mathematics
Issue number1
StatePublished - Aug 2009
Externally publishedYes

Bibliographical note

Funding Information:
ACKNOWLEDGMENTS This work was partially supported by the Russian-Slovenian cooperation grant BI-RV/08-09-009. A. Guterman also acknowledges the support of the Russian Foundation for Basic Research, project no. 08-01-00693a.


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