Arithmetic circuit complexity investigates the computational resources required to evaluate polynomial functions via networks of arithmetic operations. At its core, this field seeks to classify ...

We prove that if A is an algebra over a field with at least k elements, and A satisfies xk = 0, then An, the ring of n-by-n matrices over A, satisfies xq = 0, where q = kn2 + 1. Theorem 1.3 ...

Proceedings of the National Academy of Sciences of the United States of America PNAS is the world's most-cited multidisciplinary scientific serial. It publishes high-impact research reports, ...