What Does I' Represent in Zsqrt(d)?

  • Thread starter Thread starter mgsumsums
  • Start date Start date
  • Tags Tags
    Set
mgsumsums
Messages
2
Reaction score
0

Homework Statement



Show I' ideal in Zsqrt(d)
Let I'=I intersection Z (where Z denotes the integers)
I any ideal in Zsqrt(d)

Homework Equations





The Attempt at a Solution


I think I' is just the set of integers in Z such that the integer is an ideal of zsqrt(d)
But how is this ideal since if I left or right multiply any element of zsqrt(d) with an element in I' I get an elementary with an imaginary component?

 
Physics news on Phys.org
Problem solved prof made a typo sorry
 

Thread 'Prove that the integral is equal to ##\pi^2/8##'

Prove $$\int\limits_0^{\sqrt2/4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx = \frac{\pi^2}{8}.$$ Let $$I = \int\limits_0^{\sqrt 2 / 4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx. \tag{1}$$ The representation integral of ##\arcsin## is $$\arcsin u = \int\limits_{0}^{1} \frac{\mathrm dt}{\sqrt{1-t^2}}, \qquad 0 \leqslant u \leqslant 1.$$ Plugging identity above into ##(1)## with ##u...
View full post »

Similar threads

Integral Domains: Homework Statement & Equations
Replies
3
Views
1K
Proving that lcm(a,b)gcd(a,b)=ab
Replies
8
Views
3K
Showing that a set is an ideal
Replies
7
Views
2K
Prove that the roots of unity is a cyclic group
Replies
10
Views
2K
Operation on Sets Homework: B-A & C-A
Replies
7
Views
2K
Is the set open, closed, neither, bounded, connected?
Replies
7
Views
3K
Find the volume bounded by hyperboloid and plane z = ± d
Replies
14
Views
2K
Prove that ##\lim\limits_{x \to \infty} f(x) = 0##
Replies
3
Views
580
Prime ideal question (abstract algebra)
Replies
4
Views
2K
Examples of Partitions: How to Divide Nonzero Integers into Infinite Sets?
Replies
5
Views
2K

Hot Threads

Recent Insights

Back
Top