# Course

## MA602 - Algebra II

Course No:
MA602
Credit:
8
Approval:
2018
PG-Core
Syllabus:
Linear Algebra: Matrix of a Linear transformation, dual vector spaces, determinants, Tensor algebras, Symmetric algebras, Exterior algebras,

Modules over PIDs: Basic theory, Structure theorem for finitely generated abelian groups, Rational and Jordan canonical forms.

Field Theory: Algebraic extensions, Splitting fields, Algebraic closures, Separable and Inseparable extensions, Cyclotomic polynomials and extensions, Galois extensions, Fundamental Theorem of Galois theory, Finite fields, Composite extensions, Simple extensions, Cyclotomic extensions and Abelian extensions over rational field, Galois groups of polynomials, Fundamental theorem of algebra, Solvable and Radical extensions, Computation of Galois groups over rational field.

Reference Books:
1. D. S. Dummit and R. M. Foote, Abstract Algebra. John Wiley & Sons, 2004.
2. T. W. Hungerford, Algebra, Graduate Texts in Mathematics, 73, Springer, 1980.
3. M. Artin, Algebra, Prentice Hall, 1991.
4. T. T. Moh: Algebra, World Scientic, 1992
5. N. Bourbaki, Algebra, Springer, 1989.