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.

Prerequisites: Basics of Set Theory and Integers.- Groups: Introductory Concepts.- Actions of Groups, Topological Groups and semigroups.- Rings: Introductory Concepts.- Ideals of Rings: Introductory concepts.- Factorization in Integral Domains and in Polynomial Rings.- Rings with Chain Conditions.- Vector Spaces.- Modules.- Algebraic Aspects of Number Theory.- Algebraic Numbers.- Introduction to Mathematical Cryptography.- Appendix A: Some Aspects of Semirings.- Appendix B: Category Theory.- Appendix C: A Brief Historical Note.                                                                                                                                               

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.                                                                                                                                  

“I want to note explicitly that his treatment of what universality means in this context is particularly well done … It is also noteworthy that right after discussing fiber bundles in this fifth chapter, Adhikari goes on to the massively important topic of vector bundles, stressing right off the bat that “their homotopy classifications play a very important role in mathematics and physics.” … It is rather comprehensive (at around 600 pages it would be difficult to avoid this), and it shows very good taste on the author’s part as far as what he’s chosen to do and how he’s chosen to do it…Wow! What a nice book.” (Michael Berg, MAA Reviews, February, 2017)“This fairly thick (more than 600 pages long) book covers a lot of topics that are not generally taught to American undergraduates at all. … This book is certainly an unusual one, filled with interesting material, and there are quite a few exercises spanning a wide range of difficulty. … have considerable value as a reference for undergraduate or graduate professors, or advanced students … .” (Mark Hunacek, MAA Reviews, March, 2014) “This book gives an accessible presentation on Basic Modern Algebra with Applications … at the undergraduate level. Each chapter has interesting exercises and additional reading. … It is an interesting book which reveals the importance of modern algebra concepts in contemporary mathematics.” (Corina Mohorianu, zbMATH, Vol. 1284, 2014) "This is a rather unusual book. intended as a text on modern algebra for undergraduate mathematics students, the book covers a vast area including many topics which are far too advanced for an undergraduate course, yet omitting some useful and important subjects such as simple groups, cyclotomy and Galois theory… book is basic only in the sense that it starts from the beginning in many topics being covered, but the learning curve is very steep in most places."(Peter Shiu, The Mathematical Gazette, Volume 99, Issue 544,March 2015)                                   

Presents self-contained algebra text for independent study Provides problem-solving techniques for better grasp of the topic Discusses applications of algebra to number theory, primality testing, cryptography, geometry and topology? Includes supplementary material: sn.pub/extras