MA3102 : Algebra I (Autumn 2018) | Academic Portal of IISER Kolkata

Details of MA3102 (Autumn 2018)

Level: 3

Type: Theory

Credits: 4.0

Course Code	Course Name	Instructor(s)
MA3102	Algebra I	Somnath Basu

Syllabus
Groups : Definition of groups, subgroups, group homomorphisms and isomorphisms, normal subgroups, quotient groups, Lagrange's theorem, isomorphism theorems, direct sum of abelian groups, direct products, group actions, conjugacy classes, orbits and stabilizers, class equations, symmetric groups, simple groups, simplicity of $A_n$ with $n>4$, Sylow's theorems, classification of finitely generated abelian groups. Rings : Definition of ring with examples, homomorphism theorems, ideals (definition and examples).

Syllabus

Groups : Definition of groups, subgroups, group homomorphisms and isomorphisms, normal subgroups, quotient groups, Lagrange's theorem, isomorphism theorems, direct sum of abelian groups, direct products, group actions, conjugacy classes, orbits and stabilizers, class equations, symmetric groups, simple groups, simplicity of $A_n$ with $n>4$, Sylow's theorems, classification of finitely generated abelian groups.
Rings : Definition of ring with examples, homomorphism theorems, ideals (definition and examples).

References
Artin, M., Algebra, Prentice-Hall. Dummit, D.S. and Foote, R.M., Abstract Algebra, Wiley. Fraleigh, J.B., A First Course in Abstract Algebra, Narosa Publishers. Gopalakrishnan, N.S., University Algebra, New Age International. Herstein, I.N., Topics in Algebra, Wiley. Hungerford, T.W., Algebra, Springer-Verlag. Musili, C., Introduction to Rings and Modules, Narosa Publishers. Malik, D.S., Mordeson, J.M. and Sen, M.K., Fundamentals of Abstract Algebra, McGraw-Hill.

References

Artin, M., Algebra, Prentice-Hall.
Dummit, D.S. and Foote, R.M., Abstract Algebra, Wiley.
Fraleigh, J.B., A First Course in Abstract Algebra, Narosa Publishers.
Gopalakrishnan, N.S., University Algebra, New Age International.
Herstein, I.N., Topics in Algebra, Wiley.
Hungerford, T.W., Algebra, Springer-Verlag.
Musili, C., Introduction to Rings and Modules, Narosa Publishers.
Malik, D.S., Mordeson, J.M. and Sen, M.K., Fundamentals of Abstract Algebra, McGraw-Hill.

Sl. No.	Programme	Semester No	Course Choice
1	IP	1	Core
2	IP	3	Not Allowed
3	IP	5	Not Allowed
4	MR	1	Not Allowed
5	MR	3	Not Allowed
6	MS	5	Core
7	RS	1	Not Allowed
8	RS	2	Not Allowed