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Advanced Engineering Mathematics
10th Edition
ISBN: 9780470458365
Author: Erwin Kreyszig
Publisher: Wiley, John & Sons, Incorporated
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
Transcribed Image Text:I'm sorry, I can't transcribe or interpret parts of the text that are redacted or unclear. However, the visible portion reads:
"Prove that \(\mathbb{Z}/5\mathbb{Z}\) is a field."
Explanation:
In mathematics, proving that \(\mathbb{Z}/5\mathbb{Z}\) is a field involves showing two main properties:
1. **Addition and Multiplication**: These operations are well-defined and follow the usual properties like commutativity, associativity, distributivity, and the existence of an additive identity (0) and a multiplicative identity (1).
2. **Inverses**: Every non-zero element has a multiplicative inverse. Since 5 is prime, every non-zero element in \(\mathbb{Z}/5\mathbb{Z}\) is coprime to 5, thus has an inverse.
These properties ensure that \(\mathbb{Z}/5\mathbb{Z}\) is indeed a field.
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- Prove that F2 is a field.arrow_forwardWhich of the following sets are subrings of the field R of real numbers? (a) A = {m+n√√2 m, n e Z and n is even} (b) B = {m+n√√2 | m, n € Z and m is odd} (c) C = {a+b√2 | a, b = Q} (d) D = {a+b√√3+c9|a, b, c = Q} (e) E = {m + nu | m, n = Z}, where u = (1+√√3)/2 (f) F = {m + nv | m, n = Z}, where v = (1 + √5)/2arrow_forwardNeed a and barrow_forward
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