Course

M302 - Rings and Modules

Course No: 
M302
Credit: 
4
Prerequisites: 
M202
Approval: 
2014
UG-Core
Syllabus: 
Rings, ideals, quotient rings, ring homomorphisms, isomorphism theorems, prime ideals, maximal ideals, Chinese remainder theorem, Field of fractions, Euclidean Domains, Principal Ideal Domains, Unique Factorization Domains, Polynomial rings, Gauss lemma, irreducibility criteria.
Modules, submodules, quotients modules, module homomorphisms, isomorphism theorems, generators, direct product and direct sum of modules, free modules, finitely generated modules over a PID, Structure theorem for finitely generated abelian groups, Rational form and Jordan form of a matrix, Tensor product of modules.
Text Books: 
  1. D. S. Dummit, R. M. Foote, “Abstract Algebra”, Wiley-India edition, 2013.
Reference Books: 
  1. I. N. Herstein, “Topics in Algebra”, Wiley-India edition, 2013.
  2. M. Artin, “Algebra”, Prentice-Hall of India, 2007.

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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