MA5430 Algebra II (modified)

Course Details

Module Theory: Right and Left modules ; Examples over Z , polynomial rings and other simple rings ; Quotient modules ; module homomorphisms ; homomorphism theorems.

Ring Theory: Structure Theorem of modules over a PID ; a polynomial ring over a UFD is again a UFD ; basic properties of Noetherian rings and modules ; Universal Property of a Polynomial Ring; Quotient field and localization for integral domains.

Field Theory : Criteria for Irreducibility ; Classical Straightedge and Compass construction and examples ; normal and separable extensions.

Basic Non-Commutative Algebra: Linear Maps and Modules over non-commutative rings ; Simple and Semi-simple modules and rings.

Course References:

Text Books:
1. D. S. Dummit and R. M. Foote: Abstract Algebra, 2nd Edition, John-Wiley, 1999.
2. S. Lang: Algebra 3rd Edition, Addison-Wisely, 1999.

Reference Books:
1. J.A. Gallian: Contemporary Abstract Algebra, 4th Ed., Narosa, 1999.
2. M. Artin: Algebra, Prentice Hall inc 1994.
3. I.N. Herstein: Topics in Algebra, John-Wiley, 1995.
4. T. A. Hungerford: Algebra, Graduate Texts in Mathematics, Vol. 73, Springer-Verlag, 1980.