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.
- M. F. Atiyah, I. G. Macdonald, “Introduction to Commutative Algebra”, AddisonWesley Publishing Co., 1969.
- R. Y. Sharp, “Steps in Commutative Algebra”, London Mathematical Society Student Texts, 51. Cambridge University Press, 2000.
- D. S. Dummit, R. M. Foote, “Abstract Algebra”, Wiley-India edition, 2013.