The term "normal extension" refers to a field extension that is obtained by adjoining a root of a polynomial to a field. In certain contexts, "normal extension" may be used interchangeably with "Galois extension," which is a type of normal extension with additional properties. Some synonyms for "normal extension" include "algebraic extension," "radical extension," and "field extension by a root." These terms indicate that the extension involves adding solutions to algebraic equations. In contrast, "transcendental extension" refers to adding elements that are not algebraic over the field. Overall, the choice of synonym may depend on the specific mathematical context and the properties desired for the extension.