Course

M403 - Commutative Algebra

Course No: 
M403
Credit: 
4
Prerequisites: 
M302
Approval: 
2014
UG-Core
PG-Elective
Syllabus: 
Commutative rings, ideals, operations on ideals, prime and maximal ideals, nilradicals, Jacobson radicals, extension and contraction of ideals, Modules, free modules, projective modules, exact sequences, tensor product of modules, Restriction and extension of scalars, localization and local rings, extended and contracted ideals in rings of fractions, Noetherian modules, Artinian modules, Primary decompositions and associate primes, Integral extensions, Valuation rings, Discrete valuation rings, Dedekind domains, Fractional ideals, Completion, Dimension theory.
Text Books: 
  1. M. F. Atiyah, I. G. Macdonald, “Introduction to Commutative Algebra”, AddisonWesley Publishing Co., 1969.
Reference Books: 
  1. R. Y. Sharp, “Steps in Commutative Algebra”, London Mathematical Society Student Texts, 51. Cambridge University Press, 2000.
  2. D. S. Dummit, R. M. Foote, “Abstract Algebra”, Wiley-India edition, 2013.

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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