In this post you will be get access to download the Modern Algebra ByAR Vasishtha and AK Vasishtha Book in pdf format for free , you do not have to pay a single penny for it . Read the out the full post and get this book for free .
About the Book : –
This book is written by keeping in mind the syllabus of students currently studying in various Universities Degree, Honours, General, Subsidiary and postgraduate, I.A.S And P.C.S and for various other exams in which higher mathematics is asked. This book is really an excellent creation of a brilliant mind. This book is helpful mainly for Bsc and Msc maths students. It provides depth concepts of each and every topic through an easy and unique way . In short , It is one of the best book for modern algebra.
So , if you are interest and want to download this book in pdf format then scroll down through this page where you will see a download button clicking on that you can easily download the pdf file. If you find this article helpful then please leave a feedback in the comment section below.
CHAPTERS
01. Some Basic Set Theoretic Concepts
- Mathematical logic
- Tautologies
- Set
- Subsots 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
02. Groups
- Binary operation
- Algebraic structure
- Group. Definition
- Abolian 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 integors
- An alternative set of postulates for a group
- Permutations
- Groups of permutations
- Cyclic per mutations
- Even and odd permutations
- Integral powers of an element of a group
- Order of an element of a group
- Isomorphism 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 systens of a group
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
- homomorphismo 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
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
- Imbedding of a ring into another ring
- The field of quotients
- Ideals
- Principal ideal
- Principlal 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
- Euclidean algorithm for polynomials over a field
- Unique factorization domain
- Unique factorization theorem for polynomial over a field
- Remainder theorem
- Prime fields
- Rings of endomorphisms of an abelian group
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
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 tradsformation
- Isomorphism of vector spaces
- Quotient space
- Direct sum of spaces
- Complementary subspaces
- Co-ordinates
07. Vector Space (Continued)
- Linear transformations as vectors
- Dual space
- Dual basis
- Reflexivity
- Annihilators
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
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 tho splitting field
- Derivative of a polynomial
- Separable extension
- Perfect field
- The elements of Galois theory
- Fixed field
- Normal extension
- Galois group
- Fundamental theorem of Galois theory
- Construction with ruler and compass
- Solvability by radicals
- Finite fields
Download Modern Algebra By AR.Vasishtha & AK. VASISTHA Book pdf .
| Book Name | Modern algebra |
|---|---|
| Author | A R Vasishtha |
| Useful for | B.Sc / M.Sc / Ph.D /U.P.S.C etc.. |
| Language | English |
| Total pages | 726 |
| File size | 42.7mb |
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