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D E (ii), (iv) (v) (iv) (ii), (iii) (i) Which of the following are true ? (i): (Z7, +,-) is a field. (ii): (Z8, +,-) is a field. (iii): (Z7 x Z7, +,-) is a field. (iv): (Z2 x Z5, +, ) is an integral domain. (v): (2Z, +,-) is a field.

D E (ii), (iv) (v) (iv) (ii), (iii) (i) Which of the following are true ? (i): (Z7, +,-) is a field. (ii): (Z8, +,-) is a field. (iii): (Z7 x Z7, +,-) is a field. (iv): (Z2 x Z5, +, ) is an integral domain. (v): (2Z, +,-) is a field.

Advanced Engineering Mathematics
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:** Which of the following are true? (i) \( (\mathbb{Z}_7, +, \cdot) \) is a field. (ii) \( (\mathbb{Z}_8, +, \cdot) \) is a field. (iii) \( (\mathbb{Z}_7 \times \mathbb{Z}_7, +, \cdot) \) is a field. (iv) \( (\mathbb{Z}_2 \times \mathbb{Z}_5, +, \cdot) \) is an integral domain. (v) \( (2\mathbb{Z}, +, \cdot) \) is a field. **Options:** - A: (ii), (iv) - B: (v) - C: (iv) - D: (ii), (iii) - E: (i)
Transcribed Image Text:**Question:** Which of the following are true? (i) \( (\mathbb{Z}_7, +, \cdot) \) is a field. (ii) \( (\mathbb{Z}_8, +, \cdot) \) is a field. (iii) \( (\mathbb{Z}_7 \times \mathbb{Z}_7, +, \cdot) \) is a field. (iv) \( (\mathbb{Z}_2 \times \mathbb{Z}_5, +, \cdot) \) is an integral domain. (v) \( (2\mathbb{Z}, +, \cdot) \) is a field. **Options:** - A: (ii), (iv) - B: (v) - C: (iv) - D: (ii), (iii) - E: (i)
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