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3rd December 2014, 12:26 PM
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Join Date: Apr 2013
Re: Annamalai University MSc Mathematics 1st Year Exam Question Paper

Here is the list of few questions of Annamalai University MSc Mathematics 1st Year Exam Sample Question Paper which you are looking for .

1. Show that the relation a ≡ b mod H is an
equivalance relation.
2. Let G be a group, H a subgroup of G, T an
automorphism of G. Let (H)T = { hT/h ∈ H}.
Prove that (H)T is subgroup of G.
4
(b) Show that K is a normal extension of F if
and only if, K is the splitting field of some
polynomial over F.
15. (a) Show that the linear transformation T on
V is unitary if and only if, it takes an
orthonormal basis of V into an
orthonormal basis of V.
(b) Show that for every prime p and every
positive integer m, there is a unique field
having pm elements.
2 3
3. Show that a fininte integral domain is a field.
4. Let R be a Euclidean ring and A be an ideal of
R. Show that A = { a0 x / x ∈ R} where a0 ∈ A.
5. Show that if V is the internal direct sum of υ1,
υ2,....... υn then V is isomorphic to the the
external direct sum of υ1, υ2...... υn




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