Question 5.►(a) Prove that the field Z3, O, O is not algebraically closed.(b) Given the set Q of all matrices in M(2, C) that have the formW ZShow that the triple < 2, +, > is a division ring.(c) In the ring Z, O, O, how many different polynomials are there of degree less thannEN? How many different monic polynomials are there of degree n E N? How manydifferent polynomials are there of degree n EN?R, +, and S = S, #, * are commutative rings, and R~ S.(d) Prove that if R =then R[r]~ S[r].for z, w ECQuestion 6.

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Answered: (a) Prove that the field Z3, 0, > is…

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter8: Polynomials

Section8.3: Factorization In F [x]

Problem 21E: Prove the Unique Factorization Theorem in (Theorem). Theorem Unique Factorisation Theorem Every...

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(a) Prove that the field Z3, 0, > is not algebraically closed.