Modern Algebra by A R Vasishtha PDF Download 2023 [Krishna Series]

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.

Then download the Modern Algebra by A R Vasishtha Book in PDF format, the direct link is given below.

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》Mathematical logic
》Tautologies
》Set
》Subsets of a set
》Union of sets
》Intersection of sets
》Cartesian product of two sets
》Functions or mappings
》Binary operation
》Relations
》Equivalence relations
》Equivalence classes
》Partitions
》Partial order relations
Chapter 02. Groups》Binary operation
》Algebraic structure
》Group. Definition
》Abelian group
》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
》Permutations
》Groups of permutations
》Cyclic 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
》Co-sets
》Relation of congruence modulo
》Lagrange’s theorem
》Euler’s theorem
》Fermat’s theorem
》Order of the product of  2 subgroups of finite order
》Cayley’s theorem
》Cyclic groups
》Subgroup generated by a subset of a group
》Generating systems of a group        
Chapter 03. Groups (Continued)》Normal subgroups
》Conjugate elements
》Normalizer of an element of a group
》Class equation of a group
》Centre of a group
》Conjugate subgroups
》Invariant subgroups
》Quotient groups
》Homomorphism of groups
》Kernel of a homomorphism
》Fundamental theorem on homomorphism of groups
》Automorphisms of a group
》Inner automorphisms
》More results on group homomorphism
》Maximal supergroups
》Composition series of a group and the Jordan-Holder theorem
》Solvable groups
》Commutator subgroup of a group
》Direct products
》External direct products
》Internal direct products
》Cauchy’s theorem on abelian groups
》Cauchy’s theorem
》Sylow’s theorem       
Chapter 04. Rings》Ring. Definition
》Elementary properties of a ring
》Rings with or without 0 divisors
》Integral domain
》Field
》Division ring or skew field
》Isomorphism of rings
》Subrings
》Subfields
》Characteristic of a ring
》Ordered integral domains
》Embedding of a ring into another ring
》The field of quotients
》Ideals
》Principal ideal
》Principal ideal ring
》Divisibility in an integral domain
》Units
》Associates
》Prime elements
》Greatest common divisor
》Polynomial rings
》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
》Remainder theorem
》Prime fields
》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
》Maximal ideals
》Prime ideals
》Euclidean rings or Euclidean domains
》Polynomial rings over unique factorization domains      
Chapter 06. Vector Space》Vector space Definition
》General properties of vector spaces
》Vector subspaces
》Linear combination of vectors
》Linear span
》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
》Quotient space
》Direct sum of spaces
》Complementary subspaces
》Co-ordinates      
Chapter 07. Vector Space (Continued)》Linear transformations as vectors
》Dual space
》Dual basis
》Reflexivity
》Annihilators       
Chapter 08. Modules》Modules. Definition
》Submodules
》Direct sum of submodules
》Homomorphism of modules or linear transformations
》Quotient modules
》Cyclic modules
》Fundamental theorem on finitely generated  modules over Euclidean rings
Chapter 09. Extension Fields and Galois Theory》Field extensions
》Finite field extension
》Field ad-junctions
》Simple field extension
》Algebraic field extensions
》Transcendental element
》Roots of polynomials
》Multiple roots
》Splitting field or decomposition field
》Uniqueness of the splitting field
》Derivative of a polynomial
》Separable extension
》Perfect field
》The elements of Galois’s theory
》Fixed field
》Normal extension
》Galois group
》Fundamental theorem of Galois theory
》Construction with ruler and compass
》Solvability by radicals
》Finite fields      
Index

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