Fundamentals of Abstract Algebra

Sets, relations and integers introduction to groups permution groups subgroups and normal subgroups homomorphisms and isomorphisms of groups sylow theorem solvable and nilpotent groups finitely generated abelian groups introduction to rings subrings, ideals and homomorphisms extensions of rings direct sum of rings polynomial rings eculidean rings unique factorization domains maximal, prime and primary ideals noetherian and artinian rings modules and vector spaces matrix rings field extensions algebraic extensions multiplicity of roots finite fields Galois theory and applications normal extensions geometric constructions binary codes Groebner bases answers and hints to selected exercises.

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