MA5320 Algebra 1
Review of basic Group Theory, Direct sum and direct product of groups, Group Actions, Cayley's Theorem, The Class Equation, Sylow's Theorems (15 lectures)
Review of basic Ring Theory, Properties of Ideals, Prime and Maximal Ideals, Two-sided ideals and Quotient Rings, Chinese Reminder Theorem, Euclidean Domain, Euclidean Algorithm, Principal Ideal Domain, Euclidean Domain is a Principal Ideal Domain, UFD, PID implies UFD. (20 lectures)
Field extensions, basic properties of degree of field extensions. (5 lectures)
1. D. S. Dummit and R. M. Foote: Abstract Algebra, 2nd Edition, John-Wiley, 1999.
2. S. Lang: Algebra 3rd Edition, Addison-Wesley, 1999.
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.