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14 Result(s)
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Avishek Adhikari
Algebra
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Chapter and Conference Paper
Computationally Secure Robust Multi-secret Sharing for General Access Structure
Secret sharing scheme plays a crucial role in distributed cryptosystems. Due to its extensive use in numerous applications, an important goal in this area is to minimize trust among the participants. To remove...
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Book
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Chapter
Prerequisites: Basics of Set Theory and Integers
Chapter 1 studies some basic concepts of set theory and some properties of integers which are used throughout the book and in many other disciplines. Set theory occupies a very prominent place in modern scienc...
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Chapter
Actions of Groups, Topological Groups and Semigroups
Chapter 3 discusses actions of semigroups, groups, topological groups, and Lie groups. Each element of a group determines a permutation on a set under a group action. For a topological group action on a topolo...
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Chapter
Ideals of Rings: Introductory Concepts
Chapter 5 continues the study of theory of rings, and introduces the concept of ideals which generalize many important properties of integers. Ideals and homomorphisms of rings are closely related. Like normal...
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Chapter
Algebraic Aspects of Number Theory
Chapter 10 discusses some more interesting properties of integers, in particular, properties of prime numbers and primality testing by using the tools of modern algebra, which are not studied in Chap. ...
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Chapter
Rings with Chain Conditions
Chapter 7 continues to develop the theory of rings and studies chain conditions for ideals of a ring. The motivation came from an interesting property of the ring of integers Z that its every ascending chain of i...
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Chapter
Introduction to Mathematical Cryptography
Chapter 12 presents applications and initiates a study on cryptography. In the modern busy digital world, the word “cryptography” is well known. Every day, knowingly or unknowingly, in many places different te...
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Chapter
Modules
Chapter 9 initiates module theory, which is one of the most important topics in modern algebra. It is a generalization of an abelian group (which is a module over Z) and also a natural generalization of a vector ...
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Chapter
Groups: Introductory Concepts
Chapter 2 gives an introduction to the group theory. This concept is used in subsequent chapters. Groups serve as one of the fundamental building blocks for the subject called today modern algebra. The theory ...
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Chapter
Rings: Introductory Concepts
Rings also serve as a fundamental building blocks for modern algebra. Chapter 4 introduces the concept of rings, another fundamental concept in the study of modern algebra. A group is endowed with only one bin...
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Chapter
Factorization in Integral Domains and in Polynomial Rings
Chapter 6 extends to rings the concepts of divisibility, greatest common divisor, least common multiple, division algorithm, and Fundamental Theorem of Arithmetic for integers with the help of theory of ideals...
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Chapter
Algebraic Numbers
Chapter 11 introduces algebraic number theory which developed through the attempts of mathematicians to prove Fermat’s Last Theorem. An algebraic number is a complex number which is algebraic over the field Q of ...
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Chapter
Vector Spaces
Chapter 8 introduces another algebraic system, called vector spaces (linear spaces) interlinking both internal and external operations. In this chapter vector spaces and closely related fundamental concepts, s...
