Purchase Solution

Subrings and Division Rings

Not what you're looking for?

Ask Custom Question

Prove that any finite subring of a division ring is a division ring.

Purchase this Solution
Solution Summary

Subrings and Division Rings are investigated. The solution is detailed and well presented.

Solution Preview

let R be a division ring, and S a finite subring of R with a 1.

observe that a unit of any ring with identity cannot be a zero divisor; to this end, suppose that a is a unit; ...

Purchase this Solution
Free BrainMass Quizzes
Graphs and Functions

This quiz helps you easily identify a function and test your understanding of ranges, domains , function inverses and transformations.

Probability Quiz

Some questions on probability

Solving quadratic inequalities

This quiz test you on how well you are familiar with solving quadratic inequalities.

Multiplying Complex Numbers

This is a short quiz to check your understanding of multiplication of complex numbers in rectangular form.

Exponential Expressions

In this quiz, you will have a chance to practice basic terminology of exponential expressions and how to evaluate them.

View More Free Quizzes
Related BrainMass Solutions

  • Rings, Commutative Rings, Idempotents, Subrings and Isomorphisms

    41110 Rings, Commutative Rings, Idempotents, Subrings and Isomorphisms (1) Given a ring R, an element e is called an idempotent if e^2 = e. (i) Let R1 and R2 be two commutative rings with unity. Consider R = R1 x R2.

  • Rings and groups

    There are several questions regarding rings, groups, subrings, and quaternions. Example: Let R be a ring and [equationA]. Let [equationB] be the ring of n x n matrices with entries in R. What is the identity element of S?

  • Commutative Rings, Subrings and Submodules

    117590 Commutative Rings, Subrings and Submodules Problem: I need to show that (i) leads to (ii), then (ii) leads to (iii): Let S be a commutative ring, R be a subring in S and x be an element from S.

  • Rings and Subrings

    Then we have Rings and Subrings are investigated. The solution is detailed and well presented.

  • Commutative ring proofs

    This provides examples of proofs regarding commutative rings and equivalence relations and classes, subrings and monomorphisms, units, and isomorphism.

  • Continuous Real Functions and Subrings

    Continuous real functions and subrings are investigated. The solution is detailed and well presented.

  • 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.]

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

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

  • 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.

View More Related Solutions