Panjab University M.Sc. in Mathematics under the framework of Honours School System Syllabus


Semester-I
Core Course-I
MAT MC1: Field Theory & Commutative Algebra-I
[7 hrs/per week (including Tutorials)]
[Max. Marks: 100]
(Final-80+Internal Assessment-20)
Time : 3hrs


UNIT-I
Field Theory: Fields, Examples, Algebraic and Transcedental elements. The degree of a
field extension. Adjunction of roots. Splitting fields. Finite fields. Algebraically closed fields.
Separable and purely inseparable extensions.

UNIT-II
Perfect fields, primitive elements, Lagrange’s theorem on primitive elements. Normal
extensions, Galois extensions, The fundamental theorem of Galois Theory.

UNIT-III
Symmetric functions. Cyclotomic extensions. Cyclic extensions, Norms and traces. Quintic
Equations and solvability by radicals.

UNIT-IV
Review of Rings and ring homomorphism, ideals, quotient rings, zero divisors, nilpotent
elements, units, prime ideals and maximal ideals, Nilradical and Jacobson radical,
operation on ideals, extension and contraction of ideals, Modules and module
homomorphisms, submodule and quotient module, operation on submodules, direct sum
and product, finitely generated modules, exact sequences, tensor product of modules,

Attached Files

Panjab University M.Sc. in Mathematics under the framework of Honours School System Syllabus.pdf (780.5 KB, 72 views)