Abstract Algebra Study Materials 2021 – Download Unit wise PDFs & Imp Questions

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Abstract Algebra Study Materials: Download Abstract Algebra Study Materials 2021. In this article Abstract Algebra Study Materials, we are going to provide Study Notes for the School of Sciences. This subject is very important for B.Sc (Mathematics). This subject covers the topics of Elementary Group Theory, Elementary Ring Theory, Integral Domains, Elementary Ring Theory, etc. Through this article, you can download Unit wise PDFs, Chapters, Topics, and Important Questions. Read the below article Abstract Algebra Study Materials, to download the material PDFs.

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Abstract Algebra Study Materials - Download Study Books PDF

Abstract Algebra Study Materials

Abstract algebra is the set of advanced topics of algebra that deal with abstract algebraic structures rather than the usual number systems. The most important of these structures are groups, rings, and fields.

  • Solving of¬†systems of linear equations, which led to¬†linear algebra
  • Attempts to find formulas for solutions of general¬†polynomial¬†equations of higher degree that resulted in discovery of¬†groups¬†as abstract manifestations of¬†symmetry
  • Arithmetical investigations of quadratic and higher degree forms and¬†diophantine equations, that directly produced the notions of a¬†ring¬†and¬†ideal.
Name of the Subject Abstract Algebra 
Category School of Sciences
Useful for Bachelor of Science
Course Type Under Graduation Courses
Article on Abstract Algebra Study Materials 2021
Study Material Format PDF
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Abstract Algebra Study Books

The books given here are the best books for gaining good knowledge in Abstract algebra.

Subject  Download Links 
Abstract Algebra Download 
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Chapters & Topics

In algebra, which is a broad division of mathematics, abstract algebra is the study of algebraic structures. Algebraic structures include groups, rings, fields, modules, vector spaces, lattices, and algebras. Because of its generality, abstract algebra is used in many fields of mathematics and science.

Elementary Group Theory

  • Lagrange’s Theorem
  • Subgroups
  • Groups
  • Sets and Functions

Some More Group Theory

  • Finite Groups
  • Permutation Groups
  • Group Homomorphisms
  • Normal Subgroups

Elementary Ring Theory

  • Ring Homomorphisms
  • Subrings and Ideals
  • Rings

Integral Domains and Fields

  • Irreducibility and Field Extensions
  • Special Integral Domains
  • Polynomial Rings
  • The Basics

Subjects in the Universities

This subject will be useful to the students who are pursuing a Bachelor of Science. The following university students can also download Abstract Algebra study materials :

  • IGNOU
  • Uttarakhand Open University
  • University of Calicut
  • Pondicherry University

Subjects in the Semesters

Because of its generality, abstract algebra is used in many fields of mathematics and science. For instance, algebraic topology uses algebraic objects to study topologies. Abstract Algebra subject will be studied by the students in the following semesters of their respective courses :

  • B.Sc Mathematics III Semester

Unit wise PDFs

Download Unit wise PDFs of Abstract Algebra subject :

Units  Download Links 
Elementary Group Theory Download
Some More Group Theory Download
Elementary Ring Theory Download
Integral Domains and Fields Download

Important Questions

We have mentioned some of the important questions of Abstract Algebra subject :

  • What is the inverse of f: R -> R: f(x) = x/3?
  • In each of the following questions, both f and g are functions from R + R. Define f o g and g o f.
    • f(x) = 5x, g(x) = x + 5
    • f(x) = 5x, g(x) = x/5
    • f(x) = 1 x I, g(x) = x¬≤.
  • If A x B = ( (7,2), (7, 3). (7,4), (2,2), (2,3), (2,4) ), determine A and B.
  • For any subsets A. B, C of a set S, show that
    • (A‚ą™B)‚ą™C=A‚ą™(B‚ą™C)
    • (A‚ą©B)‚ą©C =A‚ą©(B‚ą©C)
    • A‚ą™(B‚ą©C)=(A‚ą™B)n(A‚ą™C)
    • A‚ą©(B‚ą™C)=(A‚ą©B)‚ą™(A‚ą©C)
  • Let R be a ring with unity 1 and char R =m. Define f : Z + R : f(n) = n. I. Show that f is a homomorphism. What is Kerf?
  • Show that. in F is associative, commutative, distributive over +, and [1,1] is the multiplicative identity for F.
  • The polynomial x4’+ 4 can be factored into linear factors in Z5 [x]. Find this factorization.¬†

Recommended books for Abstract Algebra

The books that are useful for knowing about Abstract Algebra are given here. These are available online and can be downloaded for learning.

  • Abstract Algebra: Theory and Applications,¬† by¬†Thomas W Judson, Hardcover Publication
  • Concrete Abstract Algebra: From Numbers to Grobner Bases, by¬†Niels Lauritzen, Paperback Publication

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