• Corpus ID: 10899498

An Introduction to Abstract Algebra

  title={An Introduction to Abstract Algebra},
  author={Andrew Klapper and Mark Goresky},
algebra plays a fundamental role in many areas of science and engineering. In this chapter we describe a variety of basic algebraic structures that play roles in the generation and analysis of sequences, especially sequences intended for use in communications and cryptography. This include groups (see Section 1.1), rings (see Section 1.2), and polynomials over rings (see Section 1.4). We also explore characters and Fourier transforms, basic tools for understanding structures based on groups and… 
The Utilize of Abstract Algebra Theory and Applications in Computer Science and Mathematics
The study of finite groups can be useful to solve combinatorial problems which sometimes arise in theory or trying to solve some real software problem.
Exploring the Beginnings of Algebraic K-Theory
According to Atiyah, K-theory is that part of linear algebra that studies additive or abelian properties (e.g. the determinant). Because linear algebra, and its extensions to linear analysis, is
Notes on the combinatorial fundamentals of algebra
This is a detailed survey – with rigorous and self-contained proofs – of some of the basics of elementary combinatorics and algebra, including the properties of finite sums, binomial coefficients,
This work is studding on computer science and its relation to abstract algebra, which is a basic method of modeling problems in many fields of computer science.
Testing of Rings and Fields Using A Computer Program
Testing of algebraic structures is expected to be easier, faster, and more accurate than manual testing by this application, which uses Cayley table as a bridge between users and the program.
On P-Polynomial Table Algebras and Applications to Association Schemes
By investigating the primitive idempotents of a commutative table algebra that has a table basis element with all distinct eigenvalues, we prove a necessary and sufficient condition in terms of the
Abstract Algebra
Algebra Abstract algebra is the study of algebraic structures and include groups, rings, fields, modules, vector spaces, lattices, and algebras. The term abstract algebra was coined in the early 20th
Exploring the beginning of Algebraic K- Theory
JETIR2108239 Journal of Emerging Technologies and Innovative Research (JETIR) www.jetir.org b871 Exploring the beginning of Algebraic KTheory Alok Prasad Rout, N. Jagannadham Research Scholar,
Classification of Finite Fields with Applications
We present a formalisation of the theory of finite fields, from basic axioms to their classification, both existence and uniqueness, in HOL4 using the notion of subfields. The tools developed are
Presentations of groups with even length relations
  • I. Webster
  • Mathematics
    Communications in Algebra
  • 2021
Abstract We study the properties of groups that have presentations in which the generating set is a fixed set of involutions and all additional relations are of even length. We consider the parabolic


A classical introduction to modern number theory
This second edition has been corrected and contains two new chapters which provide a complete proof of the Mordell-Weil theorem for elliptic curves over the rational numbers, and an overview of recent progress on the arithmetic of elliptic curve.
THIS is a text–book intended primarily for undergraduates. It is designed to give a broad basis of knowledge comprising such theories and theorems in those parts of algebra which are mentioned in the
A course in computational algebraic number theory
  • H. Cohen
  • Computer Science, Mathematics
    Graduate texts in mathematics
  • 1993
The first seven chapters guide readers to the heart of current research in computational algebraic number theory, including recent algorithms for computing class groups and units, as well as elliptic curve computations, while the last three chapters survey factoring and primality testing methods.
Introduction to commutative algebra
* Introduction * Rings and Ideals * Modules * Rings and Modules of Fractions * Primary Decomposition * Integral Dependence and Valuations * Chain Conditions * Noetherian Rings * Artin Rings *
Finite Fields for Computer Scientists and Engineers
Euclidean Domains and Euclid's Algorithm, the Theory of m-Sequences, and the Abstract Properties of Finite Fields.
An Introduction to the Theory of Numbers
THIS book must be welcomed most warmly into X the select class of Oxford books on pure mathematics which have reached a second edition. It obviously appeals to a large class of mathematical readers.
Equations over Finite Fields
We have seen that for each prime p, there is a field F p of p elements. In fact, given any prime p and an integer r ≥ 1, there is one and only one field F q of q = p r elements. The field F q ⊇ F p
Continued fractions and linear recurrences
We prove that the numerators and denominators of the convergents to a real irrational number 0 satisfy a linear recurrence with constant coefficients if and only if 0 is a quadratic irrational. The
Continued Fractions of Algebraic Numbers
The work of the second author was supported in part by grants from the Australian Research Council and by a research agreement with Digital Equipment Corporation.
On The Shift Register Sequences
In this paper, we use firstly the method of complex and functional analysis in mathematics to obtain the vector-valued expression and some results of shift register sequences, and to establish the