ANU M.Sc in Algebra Paper 2012 Acharya Nagarjuna University Exam 2012 Test Question Paper Free Download Acharya Nagarjuna University Algebra Question Papers 2012 ANU M.Sc in Algebra Question Paper 2012 for all students Previous Year old Past Papers of ANU M.Sc in Algebra Paper 2012 Algebra Acharya Nagarjuna University Exam M.Sc in Algebra Sample Model Question Papers Free Download PDF

**Algebra**

5. Prove that every finite abelian group is the direct product of cyclic groups.

6. (a) Prove that a finite integral domain is a field.

(b) Let R be the ring of integers and let M be an ideal of R Then prove that M is maximal if and only if lvi is generated by a prime number.

7. (a) State and prove Unique factorization Theorem.

(b) If p is a prime number of the form 4n H- 1, then prove that p a2 + b2 for some integers a and b.

8. (a) State & prove Gauss lemma.

(b) If V is a finite dimensional vector space and W is a subspace of V, then

dim VJW = dim V — dim W.

9. (a) If R is a Unique tctorization domain. then prove that R [xl is also a unique factorization domain

(b) If V and V are Vector spaces, over F then show that Horn (V,W) is a Vector space over F.

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