Download Modern Algebra by A R Vasishtha PDF from here. Krishna Series Books are very popular for their explaining complex concepts in very easy student-friendly language. So, in this series of Books, ExamFlame comes up with Modern Algebra By A R Vasishtha Book which covers the M.Sc. level Abstract Algebra.
“Modern Algebra” by A. R. Vasishtha is a textbook on the topic of abstract algebra, which is the study of algebraic structures such as groups, rings, and fields. The book covers the fundamental concepts of algebra, including groups, rings, fields, and Galois theory, and it is likely intended for use in a college-level course on abstract algebra. The book also has a section on Linear Algebra which is of great importance in the field of mathematics.
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The Subject matter of this A R Vasishtha Modern Algebra book has been discussed in a very simple way that the students will find no difficulty to understand it. The book contains a large number of fully worked-out examples. The students should first try to understand the theorems and then they should try to solve the problems independently. Students must read the definition again and again for more deep clarification.
Book Features of Krishna Series Modern Algebra by A R Vasishtha
“Modern Algebra” by A. R. Vasishtha likely includes the following features:
- Clear explanations of abstract algebraic concepts, such as groups, rings, fields, and Galois theory.
- Detailed examples and exercises to help students understand and apply the concepts.
- Coverage of both the theoretical and computational aspects of abstract algebra.
- Use of numerous solved examples, illustrations, and figures to make the subject more understandable.
- A comprehensive introduction to the subject matter and the development of the subject in a logical and structured manner.
- The book is written in a style that is easy to understand and follow.
- The book also includes a number of solved and unsolved problems to help students test their understanding of the material.
- It is intended for use in a college-level course on abstract algebra.
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Download Krishna Series Modern Algebra By A R Vasishtha
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Modern Algebra by A R Vasishtha PDF: Chapter Content
The chapter content of A R Vasishtha is arranged in the table below:
|Chapter 01. Some Basic Set Theoretic Concepts
》Subsets of a set
》Union of sets
》Intersection of sets
》Cartesian product of two sets
》Functions or mappings
》Partial order relations
|Chapter 02. Groups
》Finite and infinite groups
》Order of a finite group
》General properties of groups
》Definition of a group based upon left axioms
》Composition tables for finite sets
》Addition modulo m
》Multiplication modulo p
》Residue classes of the set of integers
》An alternative set of postulates for a group
》Groups of permutations
》Even and odd permutations
》Integral powers of an element of a group
》Order of an element of a group
》somorphism of groups
》The relation of isomorphism in the set of all groups
》Complexes and subgroups of a group
》Intersection of subgroups
》Relation of congruence modulo
》Order of the product of 2 subgroups of finite order
》Subgroup generated by a subset of a group
》Generating systems of a group
|Chapter 03. Groups (Continued)
》Normalizer of an element of a group
》Class equation of a group
》Centre of a group
》Homomorphism of groups
》Kernel of a homomorphism
》Fundamental theorem on homomorphism of groups
》Automorphisms of a group
》More results on group homomorphism
》Composition series of a group and the Jordan-Holder theorem
》Commutator subgroup of a group
》External direct products
》Internal direct products
》Cauchy’s theorem on abelian groups
|Chapter 04. Rings
》Elementary properties of a ring
》Rings with or without 0 divisors
》Division ring or skew field
》Isomorphism of rings
》Characteristic of a ring
》Ordered integral domains
》Embedding of a ring into another ring
》The field of quotients
》Principal ideal ring
》Divisibility in an integral domain
》Greatest common divisor
》Polynomials over an integral domain
》Division algorithm for polynomials over a field
》Euclidean algorithm for polynomials over a field
》Unique factorization domain
》Unique factorization theorem for polynomials over a field
》Rings of endomorphisms of an abelian group
|Chapter 05. Rings (Continued)
|》Quotient rings or residue class rings
》Homomorphism of rings
》Kernel of a ring homomorphism
》Euclidean rings or Euclidean domains
》Polynomial rings over unique factorization domains
|Chapter 06. Vector Space
|》Vector space Definition
》General properties of vector spaces
》Linear combination of vectors
》Linear sum of two subspaces
》Linear dependence and linear independence of vectors
》Basis of a vector space
》Finite dimensional vector spaces
》Dimension of a finitely generated vector space
》Homomorphism of vector spaces or Linear transformation
》Isomorphism of vector spaces
》Direct sum of spaces
|Chapter 07. Vector Space (Continued)
|》Linear transformations as vectors
|Chapter 08. Modules
》Direct sum of submodules
》Homomorphism of modules or linear transformations
》Fundamental theorem on finitely generated modules over Euclidean rings
|Chapter 09. Extension Fields and Galois Theory
》Finite field extension
》Simple field extension
》Algebraic field extensions
》Roots of polynomials
》Splitting field or decomposition field
》Uniqueness of the splitting field
》Derivative of a polynomial
》The elements of Galois’s theory
》Fundamental theorem of Galois theory
》Construction with ruler and compass
》Solvability by radicals
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