Kurosh–Amitsur radical theory

Summary

Kurosh–Amitsur radical theory is the general theory of radicals of rings. A radical in this sense is a class of rings closed under homomorphic images. Every ring must have a largest ideal in the class, and the quotient by that ideal must have no nonzero ideal in the class. The Jacobson radical, the prime radical, the Levitzki radical, the upper nilradical and the Brown–McCoy radical are all examples. The theory lets one prove facts about all these radicals at once, and it extends to other algebraic structures.