Time: 9:30 - 11:00, Wednesday May 04, 2022

Venue: Room 612, A6, Institute of Mathematics, VAST

Abstract: In 1941 Jacobson proved a quaternionic fundamental theorem of algebra: Every non-constant polynomial in a central variable over the quaternion algebra admits a zero. In this talk we present a joint work with G. Alon that generalizes this result and give a Nullstellensatz for quaternionic polynomial rings, as well as a theorem for quaternionic polynomial functions . We'll then discuss recent generalizations of this result for polynomials over division algebras by Reichstein and Bao, and a generalization to matrix rings by Cimpric.