MHB Prime Ideals in K[X] - Commutative Algebra Exercise 3.22 (ii)

Math Amateur · Dec 11, 2013

I am reading R.Y.Sharp's book: "Steps in Commutative Algebra.

In Chapter 3: Prime Ideals and Maximal Ideals, Exercise 3.22 (ii) reads as follows:

-------------------------------------------------------------------------

Determine all the prime ideals of the ring K[X],

where K is a field and X is an indeterminate.

------------------------------------------------------------------------

Can someone please help me get started on this problem.

Peter

Deveno · Dec 11, 2013

$K[X]$ is a PID. So any ideal is principal.

If $P = (f(X))$ is prime, what can you say about $f(X)$?

MHB Prime Ideals in K[X] - Commutative Algebra Exercise 3.22 (ii)

Thread 'When are Markov Matrices also Martingales?'

Thread 'Derivation of equations of stress tensor transformation'

Similar threads

Hot Threads

I How to show ##p(x)=g(x)x\pm 1\in\Bbb{Q}[x]## is irreducible in ##\Bbb{Q}_{\Bbb{Z}}[x]##?

I Showing ##k[x_1,\ldots,x_n]/\mathfrak{a}## is finite dimensional

I How do we distinguish two different notations for cokernel and coimage?

I Localising a non integral domain at a prime

I ##(A/\mathfrak{a})_{\mathfrak{p}/\mathfrak{a}}## and its isomorphism?

Recent Insights

Insights Thinking Outside The Box Versus Knowing What’s In The Box

Insights Why Entangled Photon-Polarization Qubits Violate Bell’s Inequality

Insights Quantum Entanglement is a Kinematic Fact, not a Dynamical Effect

Insights What Exactly is Dirac’s Delta Function? - Insight

Insights Relativator (Circular Slide-Rule): Simulated with Desmos - Insight

Insights Fixing Things Which Can Go Wrong With Complex Numbers