Polynomial rings

Related BrainMass Solutions

• deg (f(x)g(x)) = deg f(x) + deg g(x)

  127642 deg (f(x)g(x)) = deg f(x) + deg g(x) Modern Algebra Ring Theory (XXXVIII) Polynomial Rings over Commutative Rings

• 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.

  This solution is comprised of a detailed explanation of the properties of polynomial rings over commutative rings or integral domains.

• Prove that if R is a commutative ring with unit element then R[x] is also a commutative ring with unit element.

  This solution is comprised of a detailed explanation of Polynomial Rings over Commutative Rings. It contains step-by-step explanation that R[x] is a commutative ring with unit element whenever R is.

• If R is an integral domain with unit element, prove that any unit in R[x] is a unit in R and any unit in R is also a unit in R[x].

  This solution is comprised of a detailed explanation of Polynomial Rings over Commutative Rings.

• Polynomial Rings, Module Endomorphisms and Field Isomorphisms

  155146 Polynomial Rings, Module Endomorphisms and Field Isomorphisms Please see the attached file for the fully formatted problems. Please see the attached file for the complete solution. Thanks for using BrainMass.

• If R is an integral domain with unit element, prove that any unit in R[x] must already be a unit in R.

  Modern Algebra Ring Theory (XL) Polynomial Rings over Commutative rings Integral Domain

• Euclidean algorithm, primes and unique factorization, congruences, Chinese Remainder Theorem, Hensel's Lemma, Diophantine equations, arithmetic in polynomial rings, primitive roots, quadratic reciprocity and quadratic fields.

  Topics usually include the Euclidean algorithm, primes and unique factorization, congruences, Chinese Remainder Theorem, Hensel's Lemma, Diophantine equations, arithmetic in polynomial rings, primitive roots, quadratic reciprocity and quadratic fields

• the Euclidean algorithm, primes and unique factorization, congruences, Chinese Remainder Theorem, Hensel's Lemma, Diophantine equations, arithmetic in polynomial rings, primitive roots, quadratic reciprocity and quadratic fields.

  Topics usually include the Euclidean algorithm, primes and unique factorization, congruences, Chinese Remainder Theorem, Hensel's Lemma, Diophantine equations, arithmetic in polynomial rings, primitive roots, quadratic reciprocity and quadratic fields

• If R is an Integral Domain, then so is R[x].

  This solution is comprised of a detailed explanation of the properties of polynomial rings over commutative rings or integral domains.It contains step-by-step explanation and a reference.