Course

M601 - Algebra I

Course No: 
M601
Credit: 
4
Approval: 
2014
PG-Core
Syllabus: 
Group Theory: Dihedral groups, Permutation groups, Group actions, Sylow’s theorems, Simplicity of the alternating groups, Direct and semidirect products, Solvable groups, Nilpotent groups, Jordan Holder Theorem, free groups.

Ring Theory: Properties of Ideals, Chinese remainder theorem, Field of fractions, Euclidean domains, Principal ideal domains, Unique factorization domains, Polynomial Rings, Irreducibility criteria, Matrix rings.

Module Theory: Examples, quotient modules, isomorphism theorems, Generation of modules, free modules, tensor products of modules, Exact sequences - Projective, Injective and Flat modules.

Reference Books: 
  1. D. S. Dummit and R. M. Foote, Abstract Algebra. John Wiley & Sons, 2004.
  2. T. W. Hungerford, Algebra, Graduate Texts in Mathematics, 73, Springer, 1980. 
  3. M. Artin, Algebra, Prentice Hall, 1991.

Contact us

School of Mathematical Sciences

NISERPO- Bhimpur-PadanpurVia- Jatni, District- Khurda, Odisha, India, PIN- 752050

Tel: +91-674-249-4081

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