<h3>MA5430 Algebra II (modified)</h3>
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<h4>Course Details</h4>
Module Theory: Right and Left modules ; Examples over Z , polynomial rings and other simple rings ; Quotient modules ; module homomorphisms ; homomorphism theorems.<br><br> 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.<br><br> Field Theory : Criteria for Irreducibility ; Classical Straightedge and Compass construction and examples ; normal and separable extensions.<br><br> Basic Non-Commutative Algebra: Linear Maps and Modules over non-commutative rings ; Simple and Semi-simple modules and rings.
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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-Wisely, 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.