Extension of Fields

Related BrainMass Solutions

• Show that a finite extension of fields K/k which have prime degree have only trivial subextensions.

  80989 finite extension of fields K/k which have prime degree Show that a finite extension of fields K/k which have prime degree have only trivial subextensions.

• Extension of fields proof

  192105 Extension of fields proof Let K/F be an extension of fields. Let a be an element of K such that a^2 is algebraic over F.

• Basis and Finite and Infinite Field Extensions

  Find a basis of the extension of and also calculate Let , then , , , . Thus a basis of is . Since and , then we have 2. We know already is infinite. Give an example of fields such that a) and are both infinite.

• A problem on extensions of fields

  This means that the degree is at most 2 ( the degree is the dimension of as a vector space over the field ). In general, . A problem on extension of fields are examined. The expert proves a function is odd.

• Extension of Fields and Algebraically Independent Subsets.

  164716 Extension of Fields and Algebraically Independent Subsets. Please view the attached file for proper formatting of these questions.

• Finite Fields : Field Extensions

  11374 Finite Fields : Field Extensions Please see the attached file for the fully formatted problem. Show the existence of an extension of Fq of order l for any prime l. Please see the attached file for the complete solution.

• Splitting Fields

  116040 Splitting Fields Let E be an extension of F and f(x) be in F[x]. Also, let Φ be an automorphism of E leaving every element of F fixed. Prove that Φ must take a root of f(x) lying in E into a root of f(x) in E.

• Splitting Fields : Find the splitting fields over Q for x^3+3x^2+3x-4.

  +a_n*x^n be a polynomial in K[x] of degree n>0. An extension field F of K is called a splitting field for f(x) over K if there exist elements r_1,r_2,...,r_n elements of F such that (i) f(x)=a_n(x-r_1)(x-r_2)...(x-r_n) and (ii) F=K(r_1,r_2,...

• Splitting Fields : Let F be an extension field of K of degree 2, then F is the splitting field over K for some polynomial.

  57357 Splitting Fields : Let F be an extension field of K of degree 2, then F is the splitting field over K for some polynomial. Let F be an extension field of K of degree 2, then F is the splitting field over K for some polynomial.