Determine if True/False. Write True if it is always true. Otherwise, write False. (d) A commutative ring R is a prime ideal of itself.(e) If p and q are primes, then there is a unique abelian group of order pq.

(d) A commutative ring R is a prime ideal of itself. True. Let for any two element a ,b in R ab∈R…

Answered: (d) A commutative ring R is a prime…

(d) A commutative ring R is a prime ideal of itself. (e) If p and q are primes, then there is a unique abelian group of order pq.

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter4: More On Groups

Section4.8: Some Results On Finite Abelian Groups (optional)

Problem 13E: If p1,p2,...,pr are distinct primes, prove that any two abelian groups that have order n=p1p2...pr...

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Determine if True/False. Write True if it is always true. Otherwise, write False.

(d) A commutative ring R is a prime ideal of itself.
(e) If p and q are primes, then there is a unique abelian group of order pq.

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