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.
General
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