4. Suppose K is a finite field, and let : (Z.+.0) → (K. +.0k) be the unique grouphomomorphism with (1) = 1k.a) Show that is a ring homomorphism.b) Show that ker=pZ for some prime p. p is called the characteristic of the field K.c) Show that induces an injective ring homomorphism : F→ K.d) Deduce that K is a vector space over Fp.e) Conclude that K-p" for some n.

The objective of this question is to prove several properties of a finite field K and a group…

Answered: 4. Suppose K is a finite field, and let…

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter6: More On Rings

Section6.2: Ring Homomorphisms

Problem 28E

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