Paper 2, Section II, F
(a) Consider the homomorphism given by
Describe the image of this homomorphism as an abstract abelian group. Describe the quotient of by the image of this homomorphism as an abstract abelian group.
(b) Give the definition of a Euclidean domain.
Fix a prime and consider the subring of the rational numbers defined by
where 'gcd' stands for the greatest common divisor. Show that is a Euclidean domain.
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