Syllabus
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Course Code: MMATH20-201 Course Name: Advanced Abstract Algebra |
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| MODULE NO / UNIT | COURSE SYLLABUS CONTENTS OF MODULE | NOTES |
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| 1 | Irreducible polynomials, Eisenstein criterion, Gauss lemma. Field extension, algebraic and transcendental extension, degree of an extension, algebraic closure and algebraically closed field. |
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| 2 | Splitting field, degree of extension of splitting field. Normal extension, multiple roots, prime field, characterization of prime field, finite field, separable extension. |
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| 3 | Automorphism group, fixed field, Dedekind lemma, Galois groups of polynomials, Galois extension, fundamental theorem of Galois theory, fundamental theorem of algebra, roots of unity. Cylotomic polynomials, Klein’s four group, cyclic extension, Frobenius automorphism of a finite field. |
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| 4 | Solvability of polynomials by radicals over Q. Symmetric functions and elementary symmetric functions. Construction with ruler and compass only. |
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