### MA5320 Algebra 1

#### Course Details

Group Theory:

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)

Ring Theory:

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 Theory:

Field extensions, basic properties of degree of field extensions. (5 lectures)

#### 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-Wesley, 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.