Albert's theorem

Albert's theorem states that if you have a polynomial equation with rational coefficients, and one of its roots is a number obtained by combining rational numbers and certain radical expressions (like roots), then any root involving an extension field can be expressed using similar radical operations. Essentially, it tells us that structures containing roots can be analyzed and understood through a systematic process, helping mathematicians determine how solutions relate to each other in algebraic equations. This theorem provides a foundation for understanding how radicals and field extensions work together in solving polynomial equations.