## University Algebra Through 600 Solved ProblemsProf. Gopalakrishnan Passed His B.Sc. (Hons) In Mathematics From Vivekananda College Madras In 1955 And His M.A. In The Same Subject From The University Of Madras In 1956. He Had His Early Research Training At The Tata Institute Of Fundamental Research, Bombay. He Did His Ph.D. In Homological Algebra In 1963 From The Poona University. He Has Been Teaching Algebra, Algebraic Topology, Homological Algebra And Commutative Algebra In The Poona University. He Is A Professor In The Department Of Mathematics And A Recognised Guide For Ph.D. In The University Of Poona. He Has Participated In Various National And International Symposia And Has Taught At Several Summer Institutes. He Has Published Research Papers In Scientific Journals, And Has Written A Textbook,``Commutative Algebra``. |

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a e F a e G abelian group algebraic Aut G basis characteristic polynomial characteristic roots coefficients commutative ring composition series conjugate Consider the map contains contradiction Conversely assume cyclic group defined direct product divides element of order Euclidean domain finite field G is abelian Galois extension Galois group Give an example group of order Hence G Hermitian integral domain inverse irreducible factor isomorphic Ker 9 Let ch F Let F Let G linear map linear transformation linearly independent map 9 maximal ideal minimum polynomial multiplication nilpotent non-singular non-zero normal in G normal subgroup number of elements orthogonal prime ideal proper divisor quotient field rank ring homomorphism root of unity Show that G Solution solvable splitting field subgroup of G subgroup of order subspace theorem unit element vector space zero divisors