<h3>MA5320 Algebra 1</h3>
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<h4>Course Details</h4>
Group Theory: <br>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)<br>Ring Theory:<br> 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)<br>Field Theory:<br> Field extensions, basic properties of degree of field extensions. (5 lectures)
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<h4>Course References:</h4>
Text Books:<br>
1. D. S. Dummit and R. M. Foote: Abstract Algebra, 2nd Edition, John-Wiley, 1999.<br>
2. S. Lang: Algebra 3rd Edition, Addison-Wesley, 1999.<br><br>
Reference Books:<br>
1. J.A. Gallian: Contemporary Abstract Algebra, 4th Ed., Narosa, 1999.<br>
2. M. Artin: Algebra, Prentice Hall inc 1994.<br>
3. I.N. Herstein: Topics in Algebra, John-Wiley, 1995.<br>
4. T. A. Hungerford: Algebra, Graduate Texts in Mathematics, Vol. 73, Springer-Verlag, 1980.