Rings : Elements

Related BrainMass Solutions

• Describe the Rings

  10955 Describe the Rings Please see the attached file for the fully formatted problem. Describe the rings: Z[x]/(x2 − 3, 2x + 4), Z[i]/(2 + i) where i2 = −1. Z[x]/(x^2-3, 2x+4) is isomorphic to GF(4), the field with 4 elements.

• Irreducible Elements, Additive Abelian Groups, Quotient Rings and Chinese Remainder Theorem

  Irreducible Elements, Additive Abelian Groups, Quotient Rings and Chinese Remainder Theorem are investigated.

• Rings : Fields

  The elements of rings and fields are investigated. The solution is detailed and well presented.

• Ring Theory and Cartesian Product

  additive inverse -(r,s) = (-r,-s) If R and S are nontrivial rings, show that RxS has at least 4 idempotent elements An element x of the ring is idempotent, if we have x^2=x.

• Rings

  231207 Rings: Addition and Multiplication Which of the following are rings with respect to the usual definition of addition and multiplication?

• 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

• Commutative rings and Nilpotent Elements

  Commutative rings and nilpotent elements are investigated.

• Ring Theory: Euclidean Rings and Elements with Least Common Multiples

  105914 Euclidean Rings and Elements with Least Common Multiples Given two elements a, b in the Euclidean ring R their least common multiple cЄR is an element in R such that a│c and b│c and such that whenever a│x and

• Polynomial Rings : Relatively Prime Elements

  111264 Polynomial Rings : Relatively Prime Elements Let F, K be two fields, F is a subset of K and suppose f(x), g(x) Є F[x] are relatively prime in F[x]. Prove that they are relatively prime in K[x].

• Boolean Rings, Homomorphisms, Isomorphisms and Idempotents

  maps R to a product of smaller Boolean rings which are products of Z_2 by induction, and hence so is R. Boolean Rings, Homomorphisms, Isomorphisms and Idempotents are investigated. Trivial idempotent elements are discussed.