MAMT01 Advanced Algebra M.Sc Question Bank : vmou.ac.in

Name of the University : Vardhman Mahaveer Open University
Degree : M.Sc
Department : Mathematics
Subject Code/Name : MAMT-01 – Advanced Algebra
Year : I
Document Type : Question Bank
Website : vmou.ac.in

Download Model/Sample Question Paper : https://www.pdfquestion.in/uploads/vmou.ac.in/3596.MAMT-01_42.pdf

VMOU Advance Algebra Question Paper

Time: 3 Hours
Max. Marks: 80
Note: The question paper is divided into three sections A, B & C. Write Answers as per the given instructions.

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1. Define external direct product.
2. Define internal direct product.
3. If O(H) = 2 and O(K) = 5 then find O(H×K)
4. If H and K are two sub groups of G such that G is an internal
5. Define kernel of homomorphism.
6. Define conjugate class.
7. Define normalize of an element in a group.
8. Define centre of a group.
9. Write class equation for the finite group.
10. Define commutator of two elements of a group.

11. Define derived subgroup of a group.
12. Define maximal normal subgroup of agroup.
13. Define composition series of a group.
14. Is – 6 a solvable group.
15. Define prime element in an integral domain.
16. Define Euclidean ring.
17. Define Unique factorization domain.
18. Is every Euclidean ring a principal ideal domain-
19. Is 5 an associate of 5 and -5 in (Z, +, .)
20. Define left module over a ring.
21. Define submodule.
22. Define module homomorphism.
23. Define cyclic module.
24. Is sum of two sub modules a sub module of an R-module-
25. Define linear transformation on vector spaces.
26. Define dual space of a vector space V over field F.
27. Define rank of a linear transformation on vector spaces.
28. Let V be a finite dimensional vector space and –
29. Is sum of two linear transformation a linear transformation-
30. Define field extension.
31. Define algebraic extension of a field.
32. Define simple field extension.
33. Is the field C of complex number an algebraic extenstion of R.
34. Define transcendental extension of a field.
35. Define splitting field.
36. Define normal extension of a field.
37. Define separable extension of a field.
38. Define F-automorphism for an extension field K of a field F.
39. Define perfect field.
40. Is a nonconstant polynomial over a field of characteristic zero, separable.
41. Define Galois extension of a field.
42. Define radical extension of a field.
43. Define Galois group.
44. Is the field – ( 23) a radical extension of the field Q of rational numbers-
45. Does each matrix determine a linear trabsformation-
46. Is the linear transformation determined by a matrix, i-
47. Write the type of matrix of zero map from –
48. Write type of matrix of identity map on – 5 –
49. Define the rank of a matrix.
50. Define similar matrices.

51. Define eigenvectors of a linear transformation.
52. Define eigen space of a linear transformation.
53. Define invertible matrix
54. Is rank (A) = ran (????)
55. Define multilinear function.
56. Define determinant of a matrix.
57. Define characteristics polynomial of a square matrix.
58. Define non singular matrix A A square matrix A is nonsingular if det (A) ?0
59. If A and B are similar matrices then write relation between there determinants. A det (A) = det (B)
60. Define norm of a vector
61. Write Schwartz inequality.
62. Define orthogonal vectors.
63. Write Pythogoras theorem.
64. Define adjoint of a linear transformation.
65. Define complete orthonormal set
66. Define self adont linear transformation.
67. Define orthogonal linear transformation.
68. Define orthogonal matrix.
69. Are the eigenvalues of self adjoint linear transformation real?
70. Matrix A is orthogonal, then What is value of A ????=??-1
71. Write principal axis theorem.
72. Is orthogonal matrix singular.