Want to download ALGEBRAIC STRUCTURES of B.Sc Mathematics from Madras University? Here's provided the U/ID 32355/UCME ALGEBRAIC STRUCTURES previous year 2013 Question Paper. Read the contents here and save a copy for your future reference.
Name of the university : University of Madras or Madras University
Course: B.Sc.Maths
Year: December 2013
Name of subject : ALGEBRAIC STRUCTURES
Exam Code: U/ID 32355/UCME
Time: 03 hours
Maximum : 100 marks
Also download Madras University B.C.A Digital Logic Fundamentals 2013 Question Paper
OCTOBER 2013 U/ID 32355/UCME
Time : Three hours Maximum : 100 marks
PART A — (10 × 3 = 30 marks)
Answer any TEN questions.
Each question carries 3 marks.
1. Define a normal subgroup of a group G. Can we say that every abelian group is normal?
2. Prove that a group homomorphism preserves inverses.
3. If a = (5 ,7, 9) and b = (1, 2, 3) compute a −1ba
4. Define a division ring.
5. If a ring homomorphism is an isomorphism, what can you say about its kernel?
6. Let R be a ring and a, b, c ∈ R. Prove that if a|b and a|c then a | (b + c)
7. If F is the field of real numbers, prove that the vectors (1, 1, 0, 0), (0, 1, –1, 0) and (0, 0, 0, 3) in
F^(4) are linearly independent over F.
8. If W is a subspace of a vector space V, define the annihilator of W.
9. If V is a vector space over F, u ∈V and α ∈F , prove that α u = α u .
10. Define the rank of a linear transformation.
You can see more contents in the scanned version as mathematics paper is not so easy to provide in text form...
Name of the university : University of Madras or Madras University
Course: B.Sc.Maths
Year: December 2013
Name of subject : ALGEBRAIC STRUCTURES
Exam Code: U/ID 32355/UCME
Time: 03 hours
Maximum : 100 marks
Also download Madras University B.C.A Digital Logic Fundamentals 2013 Question Paper
OCTOBER 2013 U/ID 32355/UCME
Time : Three hours Maximum : 100 marks
PART A — (10 × 3 = 30 marks)
Answer any TEN questions.
Each question carries 3 marks.
1. Define a normal subgroup of a group G. Can we say that every abelian group is normal?
2. Prove that a group homomorphism preserves inverses.
3. If a = (5 ,7, 9) and b = (1, 2, 3) compute a −1ba
4. Define a division ring.
5. If a ring homomorphism is an isomorphism, what can you say about its kernel?
6. Let R be a ring and a, b, c ∈ R. Prove that if a|b and a|c then a | (b + c)
7. If F is the field of real numbers, prove that the vectors (1, 1, 0, 0), (0, 1, –1, 0) and (0, 0, 0, 3) in
F^(4) are linearly independent over F.
8. If W is a subspace of a vector space V, define the annihilator of W.
9. If V is a vector space over F, u ∈V and α ∈F , prove that α u = α u .
10. Define the rank of a linear transformation.
You can see more contents in the scanned version as mathematics paper is not so easy to provide in text form...
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