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**About this book :- **
** Basic Modern Algebra with Applications ** written by
** Mahima Ranjan Adhikari, Avishek Adhikari **.

The book is primarily intended as a textbook on modern algebra for undergraduate mathematics students. It is also useful for those who are interested in supplementary reading at a higher level. The text is designed in such a way that it encourages independent thinking and motivates students towards further study. The book covers all major topics in group, ring, vector space and module theory that are usually contained in a standard modern algebra text.

In addition, it studies semigroup, group action, Hopf's group, topological groups and Lie groups with their actions, applications of ring theory to algebraic geometry, and defines Zariski topology, as well as applications of module theory to structure theory of rings and homological algebra. Algebraic aspects of classical number theory and algebraic number theory are also discussed with an eye to developing modern cryptography. Topics on applications to algebraic topology, category theory, algebraic geometry, algebraic number theory, cryptography and theoretical computer science interlink the subject with different areas. Each chapter discusses individual topics, starting from the basics, with the help of illustrative examples. This comprehensive text with a broad variety of concepts, applications, examples, exercises and historical notes represents a valuable and unique resource.

(Mahima Ranjan Adhikari)

**Book Detail :- **
** Title: ** Basic Modern Algebra with Applications
** Edition: **
** Author(s): ** Mahima Adhikari, Avishek Adhikari
** Publisher: ** Springer India
** Series: **
** Year: ** 2014
** Pages: ** 650
** Type: ** PDF
** Language: ** English
** ISBN: ** 978-81-322-1598-1,978-81-322-1599-8
** Country: ** India
** Get this book from Amazon**

**About Author :- **

** Mahima Ranjan Adhikari ** , IMBIC, Kolkata, West Bengal, India,

** Avishek Adhikari ** , Department of Pure Mathematics, University of Calcutta, Kolkata, West Bengal, India.

**All Famous Books of this Author :- **

Here is list all books, text books, editions, versions or solution manuals avaliable of this author, We recomended you to download all.

** • Download PDF Basic Modern Algebra with Applications by Mahima Adhikari, Avishek Adhikari **

** • Download PDF Basic Algebraic Topology and its Applications by Mahima Adhikari **

** • Download PDF Mathematical & Statistical App. in Life Sciences and Engineering by Avishek Adhikari, Mahima Adhikari **

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**Book Contents :- **
** Basic Modern Algebra with Applications ** written by
** Mahima Ranjan Adhikari, Avishek Adhikari **
cover the following topics.

1. Prerequisites: Basics of Set Theory and Integers

2. Groups: Introductory Concepts

3. Actions of Groups, Topological Groups and Semigroups

4. Rings: Introductory Concepts

5. Ideals of Rings: Introductory Concepts

6. Factorization in Integral Domains and in Polynomial Rings

7. Rings with Chain Conditions

8. Vector Spaces

9. Modules

10. Algebraic Aspects of Number Theory

11. Algebraic Numbers

12. Introduction to Mathematical Cryptography

Appendix A Some Aspects of Semirings

Appendix B Category Theory

Appendix C A Brief Historical Note

References

Index

**Note:-**

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**WORKSHEETS (Solved):- **

**SHORTCUT TRICKS (Division):- **

- Divisible by 2 Shortcut trick
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**SHORTCUT TRICKS (Prime Number):- **

- Find the prime number from 1 to 100 just in 5 second (MATH PRIME NUMBER SHORTCUT TRICK from 1 to 100 number) ?
- Find a large number "A" is prime number or not (MATH PRIME NUMBER SHORTCUT TRICK By using Square Root method) ?
- Find the composite number from 1 to 100 just in 5 second (MATH COMPOSITE NUMBER SHORTCUT TRICK from 1 to 100 number) ?