OverfieldIf is a subfield of , is called an overfield of .If are determined such that an arbitrary element of can be expressed as a linear combination of as in , then is called a base. If is finite, then is called an overfield of . If is infinite, then is an infinite overfield of . If a polynomial with root exists in with , then is algebraic. If is irreducible in , then is called a minimal polynomial. Consider as a mapping from the polynomial ring to the subring of . is a surjection homomorphism mapping, and Consider that . If can be decomposed into first-order factors in , then is called a decomposition field of . :Fields :Isomorphism mapping If , then the following expression is true: Consider that the decomposition field of is , and the decomposition field of is . In this case, the isomorphism mapping resulting from the extension of exists. When all irreducible polynomials of have a single root, is called to be separative on . [0]Top |