Central Elements of Minimal Degree in the Free Alternative Algebra

摘要

Filippov (1999) conjectured that 7 is t he minimal degree of nonzero elements in the center of the1 free alternative algebra. We prove that this conjecture is true. We give all the central elements of degree 7 in the free alternative algebra over the field ZUy.-We1 give some results that indicate that these elements are also central elements in characteristic zero.