answer letter d . Consider the ring (Z, 0, 0) where and are defined as followsab=a+b-1aob a+b-ab(a) Is the given ring commutative? Justify your answer.(b) Find the additive identity in the ring.(c) Does the ring have a unity? If yes, what is the unity? Justify our answers.(d) Is the ring a field? an integral domain? Justify your answers.

Answered: Image /qna-images/answer/963b6a53-feab-446c-ac4e-54f747a0178e.jpg

Answered: . Consider the ring (Z, 0, 0) where and…

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter6: More On Rings

Section6.4: Maximal Ideals (optional)

Problem 13E

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Since this section presents a method for constructing a field of quotients for an arbitrary integral domain D, we might ask what happens if D is already a field. As an example, consider the situation when D=5. a. With D=5, write out all the elements of S, sort these elements according to the relation , and then list all the distinct elements of Q. b. Exhibit an isomorphism from D to Q.
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