Proofs with sets
Not what you're looking for?
(See attached file for full problem description).
a) Determine the irreducibility of x20-11 over Q(set of rationals), and use it to prove or disprove that the ideal <x20-11> is a maximal ideal of Q[x].
b) Construct an integral domain R and an element a in R such that a is irreducible but not prime in R.
c) Suppose that R is a principal ideal domain and a in R is irreducible. If a does not divide b in R, prove that a and b are relatively prime.
d) Suppose p in N(set of naturals) is a prime number. Show that every element a in Zp has a p-th root, i.e. there is b in Zp with a=bp.
Purchase this Solution
Solution Summary
This solution shows how to determine irreducibility and use it in a proof of ideal, construct an integral domain and element with given characteristics, complete a proof that a and b are relatively prime, and complete a proof regarding roots of elements in a group.
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.
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.
Exponential Expressions
In this quiz, you will have a chance to practice basic terminology of exponential expressions and how to evaluate them.
Probability Quiz
Some questions on probability