AN INDEPENDENCE THEOREM AND ITS CONSEQUENCES
V. A. Ufnarovskii · Mathematics of the USSR-Sbornik · 1987
The following theorem is proved: Let be linear operators in a vector space , , and let the word be maximal in the right lexicographical order among all words of length satisfying the condition . If all the operators corresponding to the subwords of are nilpotent, then the vectors , , , ..., are independent.As a corollary, a proof is presented of Shestakov's conjecture about the number of nil-conditions necessary for a subalgebra of a matrix algebra to be nilpotent.Bibliography: 5 titles.