Course

MA601 - Algebra I

Course No: 
MA601
Credit: 
8
Approval: 
2018
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.
  4. N. Bourbaki, Algebra, Springer, 1989.
  5. C Musili, Introduction to Rings and Modules, Narosa Publishing House.
  6. N. S. Gopalakrishnan, University Algebra, New Age International

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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