For almost forty-five years, the book ';Modern Algebra' has served the student community as a textbook for introductory courses on the subject. It caters to undergraduate and postgraduate students.
The book starts from set theory and covers an advanced course in group theory and ring theory.
A detailed study of field theory and its application to geometry is undertaken after a brief and concise account of vector spaces and linear transformations. One of the chapters discusses rings with chain conditions and Hilbert's basis theorem. The book is replete with solved examples to provide ample opportunity to students to comprehend the subject.
This edition carries an improvement over all the previous editions inasmuch as it incorporates latest developments and thinking on the subject. Presentation of the subject matter has been modified in line with current thinking. Many results have been rearranged, and the proofs of many theorems rewritten. It also carries more examples now. One very perceptible change is the introduction of Multiple Choice Questions at the end of relevant chapters in keeping with the latest trend of framing questions, especially because this subject is finding place in competitive examinations as well.
1. Completely revisited. Relevant changes effected to make the subject more comprehensible
2. Proof of Schröder-Bernstein Theorem provided
3. Topic of Semi-direct Product of Groups introduced
4. Proofs of Fundamental Theorem of Arithmetic and Cauchy's Theorem for Finite Groups rewritten
5. Solutions provided to more problems
6. 124 MCQs framed in a manner that enables generation of more questions
1: Set Theory
3: Quotient Groups, Homomorphisms and Permutations
4: Structure Theory of Groups
5: Solvable Groups and Jordan-Holder Theorem
6: Survey of Some Finite Groups
8: Homomorphisms and Embedding of Rings
9: Polynomial Rings
10: Factorization Theory in Integral Domains
11: Vector Spaces
12: Linear Transformations
14: Galois Theory
15: Rings with Chain Conditions
16: Canonical Forms
• Bibliography• Index
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