Please answer number question 4 FieldsDefinition: An algebraic system {S, +, ·} consisting of a set S together with twooperations + and , is called a field if it has the following properties.Va, b, c in S:A1. Addition is associative: a + (b + c) = (a + b) + cA2.Addition is commutative: a + b= b + aАЗ.Zero: 3 an element 0 in S such that a + 0 = aA4.Opposite: 3 an element -a such that a + -a = 0M1. Multiplication is associative: a(bc) = (ab)cM2. Multiplication is commutative: ab = baM3. One: 3 an element 1 in S such that la = a1M4. Reciprocal: if a z 0,3 an clement - such that a-D.Multiplication is distributive over addition: a (b + c) = ab + ac1. Explain why the integers with + and · are not a field.2. Explain why the rational numbers with + and are a field.3. Show that the set of numbers mod 5 with e and ® is a field.4. Show that the set of numbers mod 6 with e and ® is not a field.

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Description: Please answer number question 4 FieldsDefinition: An algebraic system {S, +, ·} consisting of a set S together with twooperations + and , is called a field if it has the following properties.Va, b, c in S:A1. Addition is associative: a + (b + c) = (a

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Answered: Please answer number question 4

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Please answer number question 4

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter2: The Integers

Section2.7: Introduction To Coding Theory (optional)

Problem 12E: Suppose that the check digit is computed as described in Example . Prove that transposition errors...

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