Ring Theory : Division Rings

Related BrainMass Solutions

• Algebraic Number Theory - Definitions

  That is, a non-empty set S is said to be a field if it satisfies all the properties of a ring and is closed under division (except division by 0). [Thus, all filds are rings but all rings are not fields.]

• F[x]/(x^2 + 1) is isomorphic to the field of complex numbers

  115700 F[x]/(x^2 + 1) is isomorphic to the field of complex numbers Modern Algebra Ring Theory (XXXI) Polynomial Ring

• Subrings and Division Rings

  126499 Subrings and Division Rings Prove that any finite subring of a division ring is a division ring. let R be a division ring, and S a finite subring of R with a 1.

• Prove or disprove the existence of non-commutative division ring of order 4.

  The expert proves or disproves the existence of non-communtative division rings of order 4.

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

  Modern Algebra Ring Theory (XXXIX) Polynomial Rings over Commutative Rings Unit Element

• Division subring S = division ring D or S is a subset of D

  This solution is comprised of a detailed explanation of the problems of division rings. It contains step-by-step explanation for the problem.

• Rings and groups

  29576 Rings and Groups (Ring Theory, Quaternions, Homomorphisms, Matrices) A number of questions involving rings and groups. Example: 3) Let R be a ring and [equationA]. Let [equationB] be the ring of n x n matrices with entries in R.

• Ring Theory and Cartesian Product

  354495 Ring Theory and Cartesian Product If R and S are rings, the cartesian product RxS is a ring too with operations (r1,s1) + (r2,s2) = (r1+r2,s1+s2) (r1,s1)*(r2,s2) = (r1*r2,s1*s2) identity elements 0RxS = (0R,0s) 1RxS = (1R,1S) and

• Maximization

  348580 Ring Theory: Maximization Help 9. The Acme Class Ring Company designs and sells two types of rings: the VIP and the SST. They can produce up to 24 rings each day using up to 60 total man-hours of labor.