TRUE, S if it is SOMETIMES TRUE or F if it is FALSE. Please answer 1,2,3,4 and 5. 1.If D has no zero divisors and ab=0 in D, then a and b are both nonzero elements of D. 2. If F is a field, then F has at least 2 distinct elements. 3. If D is a UFD, then D is a PID.

TRUE, S if it is SOMETIMES TRUE or F if it is FALSE. Please answer 1,2,3,4 and 5. 1.If D has no zero divisors and ab=0 in D, then a and b are both nonzero elements of D. 2. If F is a field, then F has at least 2 distinct elements. 3. If D is a UFD, then D is a PID.

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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Question

Write A if it is always TRUE, S if it is SOMETIMES TRUE or F if it is FALSE.
Please answer 1,2,3,4 and 5.

1.If D has no zero divisors and ab=0 in D, then a and b are both nonzero elements of D.
2. If F is a field, then F has at least 2 distinct elements.
3. If D is a UFD, then D is a PID.
4. If f∈F[x] is irreducible of degree n, then f splits over some extension field K of F.
5. If (a) is a maximal ideal in a ring R, then R/(a) is an integral domain.

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