Over closed fields of prime characteristic, all algebras are quotients of group algebras (Q686413)

The aim of this paper is to prove that associative algebras are homomorphic images of group algebras (under certain restrictions). More precisely, it is shown that if \(K\) is an algebraically closed field of characteristic \(p > 0\) and \(A\) is a finite-dimensional associative algebra over \(K\), then \(A\) is a homomorphic image of the group algebra \(KG\), for some finite group \(G\).