Algebras over infinite fields, revisited (Q677442)

Theorem 1. If \(A\) is an algebra over an infinite field \(F\), \(\text{card }F>\dim A\) and the nonzero divisors of \(A\) are invertible, then \(A\) is algebraic over \(F\). -- This is a generalization of an earlier well known result of the first author (1956). Theorem 2. If \(A\) is a right FBN (fully bounded Noetherian) algebra over the algebraically closed field \(F\) with \(\text{card }F>\dim A\), then \(A\) is a PI algebra.