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Designed for undergraduate and post graduate students of mathematics, the book can also be used by those preparing for various competitive examinations. The text starts with a brief introduction to results from Set Theory and Number Theory. It then goes on to cover Groups, Rings, Vector spaces and Fields. The topics under Groups include Subgroups, Normal subgroups, Finitely generated abelian groups, Group actions, Solvable and Nilpotent groups. The course in Ring Theory covers Ideas, Imbedding of rings, Euclidean domains, Principal ideal domains, Unique factorization domains, Polynomial rings, Noetherian (Artinian) rings. The section on Vector spaces deals with Linear transformations, Inner product spaces, Dual spaces, Eigen spaces, Diagonalizable operators etc. Under Fields, Algebraic extensions, Splitting fields, Normal extensions, Separable extensions, Algebraically closed fields, Galois extensions and construction by ruler and compass are discussed. The theory has been strongly supported by numerous examples and worked out problems. There is plenty of scope also for the reader to try and solve problems on his (her) own. ISBN - 9788125919117
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