← GATE Mathematics guide GATE Mathematics · Section 6
Algebra
Group, ring and field theory — directly covered.
Books that cover Section 6
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Full syllabus — Section 6
- Groups, subgroups, normal subgroups, quotient groups, homomorphisms, automorphisms; cyclic & permutation groups; group action; finite abelian groups; Sylow’s theorems
- Rings, ideals, prime & maximal ideals, quotient rings; unique factorization, principal-ideal and Euclidean domains
- Polynomial rings; Eisenstein’s irreducibility criterion
- Fields, finite fields, field extensions, algebraic extensions, algebraically closed fields