MODULES AND RINGS-II (Optional Paper)
Paper Code:
MAT425C
Credits:
5
Contact Hours:
75.00
Max. Marks:
100.00
15.00
Local ring, Characterization of local ring, Local ring of formal power series.
15.00
Semisimple module, Semisimple ring, Characterizations of semisimple module and semisimple ring, Wedderburn-Artin theorem on semisimple ring.
15.00
Simple ring, Characterization of Artinian simple ring.
15.00
The Jacobson radical, Jacobson radical of matrix ring, Jacobson semisimple ring, Relation between Jacobson semisimple ring and semisimple ring, Hopkins-Levitzki theorem, Nakayama’s lemma, Regular ring, Relation among semisimple ring, Regular ring and Jacobson semisimple ring.
15.00
Lower nil radical, Upper nil radical, Nil radical, Brauer’s lemma, Kothe’s conjecture, Levitzki theorem.
Essential Readings:
- 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.
References:
- 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.
Academic Year:
