Rings, Prime Ideals and Maximal Ideals

Related BrainMass Solutions

• Homomorphism of Commutative Rings, Prime Ideals, Maximal Ideals

  101848 Homomorphism of Commutative Rings, Prime Ideals, Maximal Ideals Let phi:R->S be a homomorphism of commutative rings a) Prove that if P is a prime ideal of S then either phi^-1(P)=R or phi^-1(P) is a prime ideal of R.

• Ideals and Factor Rings : Prime Ideal

  17287 Ideals and Factor Rings: Prime Ideal Problem: Let R be a commutative ring. Show that every maximal ideal of R is prime and if R is finite, show that every prime ideal is maximal. ALSO is every prime ideal of Z(integers) maximal? Why?

• Quotient Rings and Maximal Ideals

  Quotient rings and maximal ideals are investigated. The solution is detailed and well presented.

• Local Rings and Maximal Ideals

  Local rings and maximal ideals are investigated.

• Ideals : Prime but not Maximal

  37878 Ideals : Prime but not Maximal Does the ring Z (integer) contain any ideals that are prime but not maximal? If so, give an example. If not, give a proof. {0} is prime ideal in Z but not maximal.

• Maximal Ideals, Cosets, Polynomials and Quotient Rings

  Maximal Ideals, Cosets, Polynomials and Quotient Rings are investigated.

• Problems Pertaining to Group Rings

  We claim that the maximal ideals of Z[G} containing I are precisely the ideals I_p for p prime, where I_n = {sum_{g in G}(a_g G) in Z[G] : n divides sum_{g in G}}. Let p be a prime. Clearly I contains I_p.

• prime ideals

  Prove directly that every maximal ideal is prime. c. For the ring of integers Z, describe all the prime ideals. Which ones are maximal, which ones are not? d.

• Maximal Ideals : Commutative Rings and Pointwise Operations ( Function Addition and Composition )

  55734 Maximal Ideals : Commutative Rings and Pointwise Operations ( Function Addition and Composition ) Let R be the set of all continuous functions from the set of real numbers into itself.