2. Let R be the commutative ring of all matrices with rational entries, M3(Q), of the forma b c0 ab00 aShow that the mapping : R Q given byab c0 ab00ais a homomorphism.$- a

For the given map to prove homomorphism.For this we prove two properties

Answered: Let R be the commutative ring of all…

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter5: Rings, Integral Domains, And Fields

Section5.2: Integral Domains And Fields

Problem 5E: Examples 5 and 6 of Section 5.1 showed that P(U) is a commutative ring with unity. In Exercises 4...

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Similar questions

Let R be the set of all matrices of the form [abba], where a and b are real numbers. Assume that R is a commutative ring with unity with respect to matrix addition and multiplication. Answer the following questions and give a reason for any negative answers. Is 12 an integral domain? Is R a field?
Consider the matrices below. X=[1201],Y=[1032],Z=[3412],W=[3241] Find scalars a,b, and c such that W=aX+bY+cZ. Show that there do not exist scalars a and b such that Z=aX+bY. Show that if aX+bY+cZ=0, then a=b=c=0.
Prove that if A is similar to B and A is diagonalizable, then B is diagonalizable.
28. a. Show that the set is a ring with respect to matrix addition and multiplication. b. Is commutative? c. does have a unity? d. Decide whether or not the set is an ideal of and justify your answer.
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Let S be the set of all 2X2 matrices of the form [x0x0], where x is a real number.Assume that S is a ring with respect to matrix addition and multiplication. Answer the following questions, and give a reason for any negative answers. Is S a commutative ring? Does S have a unity? If so, identify the unity. Is S an integral domain? Is S a field? [Type here][Type here]
11. Show that defined by is not a homomorphism.
Find a basis for R3 that includes the vector (1,0,2) and (0,1,1).
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Examples 5 and 6 of Section 5.1 showed that P(U) is a commutative ring with unity. In Exercises 4 and 5, let U={a,b}. Is P(U) a field? If not, find all nonzero elements that do not have multiplicative inverses. [Type here][Type here]

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