Noncommutative Lagrange-Fujiwara, Carmichael-Mason and Kuniyeda Bounds for Roots of Polynomials

Two centuries ago, Lagrange derived an upper bound for every root of a complex polynomial using the maximum of powers of coefficients. In 1916, Fujiwara independently found the Lagrange bound. In 1914, Carmichael and Mason derived an upper bound using the sum of squares of the absolute values of the coefficients of a polynomial. This bound was extended by Kuniyeda in 1916. We derive noncommutative versions of the Lagrange-Fujiwara, Carmichael-Mason and Kuniyeda bounds.