Integral Domains and Fields : Embedding Theorem
Not what you're looking for?
Problem:
Note: C is set containment
If R is an integral domain, show that the field of quotients Q in the Embedding Theorem is the smallest field containing R in the following sense:
If R C F, where F is a field, show that F has a sub-field K such that R C K and K is isomorphic to Q.
Purchase this Solution
Solution Summary
A proof involving fields is offered in the solution.
Solution Preview
Proof:
R is an integral domain, it means R is a commutative ring with the multiplicative unit e. Suppose R C F, where F is a field. Now we construct a map f: Q->F. For any element x=a/b in Q, ...
Purchase this Solution
Free BrainMass Quizzes
Geometry - Real Life Application Problems
Understanding of how geometry applies to in real-world contexts
Know Your Linear Equations
Each question is a choice-summary multiple choice question that will present you with a linear equation and then make 4 statements about that equation. You must determine which of the 4 statements are true (if any) in regards to the equation.
Solving quadratic inequalities
This quiz test you on how well you are familiar with solving quadratic inequalities.
Exponential Expressions
In this quiz, you will have a chance to practice basic terminology of exponential expressions and how to evaluate them.
Graphs and Functions
This quiz helps you easily identify a function and test your understanding of ranges, domains , function inverses and transformations.