Write A if it is always TRUE, S if it is SOMETIMES TRUE or F if it is FALSE. 1. If R is an integral domain, then R is a field. 2. If f∈ℝ[x], then f has at least one real root. 3. If K is a Galois extension of F, then the Galois group of K over F contains automorphisms that do not commute. 4. If f is the nth cyclotomic polynomial then f has a root in ℚ. 5. If [F:K] is a prime p, then there exists a field E such that F≤E≤K for which F≠E, E≠K.

Write A if it is always TRUE, S if it is SOMETIMES TRUE or F if it is FALSE. 1. If R is an integral domain, then R is a field. 2. If f∈ℝ[x], then f has at least one real root. 3. If K is a Galois extension of F, then the Galois group of K over F contains automorphisms that do not commute. 4. If f is the nth cyclotomic polynomial then f has a root in ℚ. 5. If [F:K] is a prime p, then there exists a field E such that F≤E≤K for which F≠E, E≠K.

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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