Practice Questions for CSIR NET Mathematics : Ring Theory
Master Key Topics with Comprehensive Multiple-Choice Questions and Detailed Solutions for CSIR NET Mathematics
1. Ring and Ideals
2. UFD, PID, and ED
3. Field Extensions
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Algebra : CSIR NET Mathematics Syllabus
- Permutations
- Combinations
- Pigeon-hole principle
- Inclusion-exclusion principle
- Derangements
- Fundamental theorem of arithmetic
- Divisibility in Z
- Congruences
- Chinese Remainder Theorem
- Euler’s Ø- function
- Primitive roots
- Groups
- Subgroups
- Normal subgroups
- Quotient groups
- Homomorphisms
- Cyclic groups
- Permutation groups
- Cayley’s theorem
- Class equations
- Sylow theorems
- Rings
- Ideals
- Prime and maximal ideals
- Quotient rings
- Unique factorization domain
- Principal ideal domain
- Euclidean domain
- Polynomial rings
- Irreducibility criteria
- Fields
- Finite fields
- Field extensions
- Galois Theory