Subsections
[Cr:4, Lc:3, Tt:1, Lb:0]
- Recapitulation: Ideals, factorization rings, prime and maximal
ideals, modules.
- Nilradical and Jacobson radical, extensions and contractions of
ideals.
- Localization of rings and modules.
- Integral dependence, integrally closed domains, going up and going
down theorem, valuation rings.
- Noetherian and Artinian rings, chain conditions on modules.
- Exact sequences of modules, tensor product, projective and injective
modules.
- Basics of categories and functors.
- Exact sequences and complexes in categories, additive functors,
derived functors EXT and TOR functors.
- Discrete valuation rings and Dedekind domains.
- M. F. Atiyah and I. G. Macdonald, Introduction to Commutative
Algebra, Addison Wesley (1969).
- Nathan Jacobson, Basic Algebra Vol. II, Dover Publications
(2009).
- Joseph J. Rotman, An Introduction to Homological Algebra, (
2nd edition), Springer (2008).
- L. R. Vermani, An Elementary Approach to Homological Algebra,
Chapman & Hall/CRC (2003).
