MODULES AND RINGS-I (Optional Paper)
Morphisms, Exact sequences, The three lemma, The four lemma, The five lemma, Butterfly of zausenhauss theorem, Product and co-product of R-modules, Free modules.
Noetherian module and Artinian module, Composition series. Projective modules, Injective modules, Direct sum of projective modules, Direct product of injective modules.
Divisible groups, Embedding of a module in an injective module, Tensor product of modules, Noetherian module and Artinian module, Finitely generated modules, Jordon-Holder theorem, Indecomposable modules, Krull–Schmidt theorem, Semi-simple modules, Submodules, Homomorphic images and direct sum of semi-simple modules.
Prime ideals, m-system, Prime radical of an ideal, Prime radical of a ring, Semi prime ideal, n-system, Prime rings, Semiprime ring as a subdirect product of a prime ring, Prime ideals and prime radical of matrix ring.
Subdirect sum of rings, Representation of a ring as a subdirect sum of rings, Subdirectly irreducible ring, Birkhoff theorem on subdirectly irreducible ring, Subdirectly irreducible boolean ring.
- T.S. Blyth, Module Theory, Clarendon Press, London, 1989.
- T.Y. Lam, Noncommutative Rings, Springer-Verlag, 1991.
- B. Hartley, T.O. Hauvkes, Rings, Modules and Linear Algebra, Chapmann and Hall Ltd., 1970.
- R.B. Allenly, Rings Fields and Graphs: An Introduction of Abstract Algebra, Edward Arnold, 1989.
- I.N. Herstein, Noncommutative Rings, C. Monographs of AMS, 1968.
- T.W. Hungerford, Algebras, Springer, 1980.
- J. Rose, A Course on Ring Theory, Cambridge University Press, 1978.
- L.H. Rowen, Ring Theory (Student Addition), Academic Press, 1991.
- N. Jacobson, Structure of Rings, AMS, 1970,
