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UNIVERSITY OF MADRAS
B.Sc. DEGREE COURSE IN MATHEMATICS
SEMESTER SYSTEM WITH CREDITS
(Effective from the Academic Year 2003-2004)
SYLLABUS
Semester V - Paper IX - Algebraic Structures I
Duration of Examination: 3 hrs
Maximum Marks: 100
Credits: 4
Groups :-
Normal subgroups; Homomorphisms; Automorphisms; Cayley's theorem; Permutation groups; Conjugacy and Class equation.
Rings :-
Definition and examples; Integral domain; homomorphism of rings; ideals and quotient rings; prime ideal and maximum ideal; the field of quotients of an integral domain; Euclidean rings; contents and treatment as in "Topics in Algebra" (I. N. Herstein , Wiley Eastern ltd.)
Chapter 2, Sections 2.6,2.7 (Omit Applications 1 and 2), 2.8, 2.9, 2.10, 2.11.
Chapter 3, Sections 3.1, 3.2, 3.3, 3.4, 3.5, 3.6, 3.7.
Reference Books :-
1. University Algebra: N. S. Gopalakrishnan (Wiley Eastern ltd.)
2. A first course in Algebra: John. B. Fraleigh (2nd Edition Addison Wesley)
3. Textbook of Algebra: R. Balakrishnan and N. Ramabadran (Vikas Publishing Co.)
4. Algebra : S. Arumugam (New Gama Publishing house, Palayankottai)
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