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The book starts with a brief introduction to results from Set theory and Number theory. It then goes on to cover Groups, Rings, Fields and Linear Algebra. The topics under groups include Subgroups, Finitely generated abelian groups, Group actions, Solvable and Nilpotent groups. The course in ring theory covers Ideals, Embedding of rings, Euclidean domains, PIDs, UFDs, Polynomial rings and Noetherian (Artinian) rings. Topics in field include Algebraic extensions, Splitting fields, Normal extensions, Separable extensions, Algebraically closed fields, Galois extensions, and Construction by ruler and compass. The portion on linear algebra deals with Vector spaces, Linear transformations, Eigen spaces, Diagonalizable operators, Inner product spaces, Dual spaces, Operators on inner product spaces etc. The theory has been strongly supported by numerous examples and workedout problems. There is also a plenty of scope for the readers to try and solve problems on their own. The book is designed for undergraduate and postgraduate students of mathematics. It can also be used by those preparing for various competitive examinations.
Designed for undergraduate and postgraduate 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, Fields and Linear Algebra. The topics under groups include subgroups, finitely generated abelian groups, group actions, solvable and nilpotent groups. The course in ring theory covers ideals, embedding of rings, Euclidean domains, PIDs, UFDs, polynomial rings, Noetherian (Artinian) rings. Topics of field include algebraic extensions, splitting fields, normal extensions, separable extensions, algebraically closed fiel...
Designed for undergraduate and postgraduate 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 (Linear Algebra) and fields. The topics under Groups include subgroups, permutation groups, finite abelian groups, Sylow theorems, direct products, group actions, solvable and nilpotent groups. The course in Ring theory covers ideals, embedding of rings, euclidean domains, PIDs, UFDs, polynomial rings, irreducibility criteria, Noetherian rings. The section on vector spaces deals with linear transformatio...
This book on Group theory for undergraduate students (Mathematics), Scholarship test (NBHM, TIFR, JEST), JRF/LS(CSIR-UGC-NET), M.Sc. entrance test (IIT-JAM), Ph.D. admission entrance test (IIT-GATE), Aspirants of Civil Services examinations (UPSC-CSE and IFS, State PCs), DRDO examinations etc. In this book all the topics of group theory are discussed with theory and suitable examples. The book is divided into eight chapters viz. groups, subgroups, normal subgroups, homomorphism, direct products in group theory, Sylow`s theorems, group actions and finite groups. All chapters containing solved examples, solution of previous years question papers of different competitive examinations UPSC(CSE), UPSC(IFS), NBHM, CSIR-UGC-NET, GATE, BPSC, IIT-JAM and exercises.
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Algebra: Abstract and Modern, introduces the reader to the preliminaries of algebra and then explains topics like group theory and field theory in depth. It also features a blend of numerous challenging exercises and examples that further enhance e
This book has been designed for Undergraduate (Honours) and Postgraduate students of various Indian Universities.A set of objective problems has been provided at the end of each chapter which will be useful to the aspirants of competitve examinations
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