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Algebra I Part A
Groups: definitions & basic examples;
Normal subgroups, quotients;
Three isomorphism theorems;
Centralizer and normalizer of a subset, centre of a group;
Permutations, symmetrc groups and Cayley’s theorem;
Group actions and their applications, Sylow’s theorems.
Rings and ideals: basic definitions, quotient rings;
The Chinese Remainder Theorem;
Maximal and prime ideals;
Unique factorization, unique factorization domains, principal ideal domains, Euclidean domains, polynomial rings;
Modules: basic definitions and examples, Hom and tensor products, the Structure Theorem for finitely generated modules over PIDs;
Fields: basic definitions and examples, algebraic & trancendental numbers;
Finite fields, characteristic, the order of a finite field.
Artin, M., Algebra, Prentice-Hall of India, 1994.
Dummit, D. S. and Foote, R. M., Abstract Algebra, John Wiley & Sons, 2001.
Herstein, I. N., Topics in Algebra, John Wiley & Sons, 1995.
Lang, S., Algebra, 3rd editiom. Springer, 2002.
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