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INDIAN INSTITUTE OF SCIENCE
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MA 212: Algebra I
Credits: 3:0
Prerequisite courses for Undegraduates: UM 203
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.
Part B
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.
Suggested books and references:
Artin,
Algebra
,M. Prentice-Hall of India, 1994.
Dummit, D. S. and Foote, R. M.,
Abstract Algebra
,McGraw-Hill, 1986.
Herstein, I. N.,
Topics in Algebra
,John Wiley & Sons, 1995.
Lang, S.,
Algebra (3rd Ed.)
,Springer, 2002.
All Courses
Contact
:
+91 (80) 2293 2711, +91 (80) 2293 2265
E-mail:
chairman.math[at]iisc[dot]ac[dot]in