15. Show that any field is isomorphic to its field of quotients. [Ilint: Make use ofthe previous exercise with f as the identity map.]16. Prove that if (R,+, ) and (R',+', ) are isomorphic integral domains, then theirfields of quotients are also isomorphic.

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Answered: 15. Show that any field is isomorphic…

15. Show that any field is isomorphic to its field of quotients. [Hint: Make use of the previous exereise with f as the identity map.]

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter5: Rings, Integral Domains, And Fields

Section5.3: The Field Of Quotients Of An Integral Domain

Problem 10E: Since this section presents a method for constructing a field of quotients for an arbitrary integral...

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Question

15. Show that any field is isomorphic to its field of quotients. [Ilint: Make use of
the previous exercise with f as the identity map.]
16. Prove that if (R,+, ) and (R',+', ) are isomorphic integral domains, then their
fields of quotients are also isomorphic.

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