Question
If $F$ is flat and $\pi: P \rightarrow F$ is a surjection with $P$ flat, prove that ker $\pi$ is flat.
Step 1
A module \( M \) is flat over a ring \( R \) if for every injective homomorphism of \( R \)-modules \( N \hookrightarrow N' \), the induced map \( M \otimes_R N \rightarrow M \otimes_R N' \) is also injective. Show more…
Show all steps
Your feedback will help us improve your experience
Joseph Liao and 75 other educators are ready to help you.
Ask a new question
Labs
Want to see this concept in action?
Explore this concept interactively to see how it behaves as you change inputs.
Key Concepts
Recommended Videos
Zero curvature Prove that the curve $$\mathbf{r}(t)=\left\langle a+b t^{p}, c+d t^{p}, e+f t^{p}\right\rangle$$ where $a, b, c, d, e,$ and $f$ are real numbers and $p$ is a positive integer, has zero curvature. Give an explanation.
Vectors and Vector-Valued Functions
Curvature and Normal Vectors
Transcript
18,000,000+
Students on Numerade
Trusted by students at 8,000+ universities
Watch the video solution with this free unlock.
EMAIL
PASSWORD