If F is a field containing an infinite number of distinct elements, the mapping f → f~ is an isomorphismof the algebra of polynomials over F onto the algebra of polynomial functions over F.

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Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter6: More On Rings

Section6.3: The Characteristic Of A Ring

Problem 22E: 22. Let be a ring with finite number of elements. Show that the characteristic of divides .

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If F is a field containing an infinite number of distinct elements, the mapping f → f~ is an isomorphism of the algebra of polynomials over F onto the algebra of polynomial functions over F.