Prove that a field is an integral domain.

Related BrainMass Solutions

• Prove that a finite integral domain is a field.

  608069 Prove that a finite integral domain is a field. Prove that a finite integral domain is field. Proof:- Let D be a finite integral domain.

• Prove or disprove that the existence of an integral domain of order 4 that is not a field.

  111491 Existence of an integral domain of order 4 that is not a field. Prove or disprove that the existence of an integral domain of order 4 that is not a field. Answer: It does not exist an integral domain of order 4 that is not a field.

• Ring theory proof

  see attached This is an example of a ring theory proof regarding field of quotients of an integral domain.

• Ideal proof

  226937 Ideals Let R be a commutative ring with 1. Prove that the principal ideal generated by x in the polynomial ring R[x] is a prime ideal if and only if R is an integral domain. Prove that (x) is a maximal ideal if and only f R is a field.

• Finite ring proofs

  Give a direct proof (i.e. without appealing to part c) that if R is an integral domain, then it is a field c.

• If R is an integral domain, then so is R[x_1, x_2, ... , x_n] . Or, Prove that if R is an integral domain, then R[x_1, x_2, ... , x_n] is also an integral domain.

  Or, Prove that if R is an integral domain, then R[x_1, x_2, ... , x_n] is also an integral domain.

• Integral domain

  21829 Integral domain There is integral domain with exactly six elements. Disprove or Prove Disprove Suppose R is an integral domain with |R|=6.

• Unique Factorization Domain with Quotient Field

  107075 Unique Factorization Domain with Quotient Field Let R be an integral domain with quotient field F and let p (X) be a monic polynomial in R[X] : Assume that p (X) = a (X) b (X) where a (X) and b (X) are monic polynomials in F [X] of smaller degree

• Ring theory proof

  98114 Ring theory proof in modern algebra Modern Algebra Ring Theory (VIII) The Field of Quotients of an Integral Domain