1 edition of **Finite Commutative Rings and Their Applications** found in the catalog.

- 184 Want to read
- 8 Currently reading

Published
**2002** by Springer US in Boston, MA .

Written in English

- Computer engineering,
- Computational complexity,
- Coding theory,
- Engineering

Foreword by Dieter Jungnickel Finite Commutative Rings and their Applications answers a need for an introductory reference in finite commutative ring theory as applied to information and communication theory. This book will be of interest to both professional and academic researchers in the fields of communication and coding theory. The book is a concrete and self-contained introduction to finite commutative local rings, focusing in particular on Galois and Quasi-Galois rings. The reader is provided with an active and concrete approach to the study of the purely algebraic structure and properties of finite commutative rings (in particular, Galois rings) as well as to their applications to coding theory. Finite Commutative Rings and their Applications is the first to address both theoretical and practical aspects of finite ring theory. The authors provide a practical approach to finite rings through explanatory examples, thereby avoiding an abstract presentation of the subject. The section on Quasi-Galois rings presents new and unpublished results as well. The authors then introduce some applications of finite rings, in particular Galois rings, to coding theory, using a solid algebraic and geometric theoretical background.

**Edition Notes**

Statement | by Gilberto Bini, Flaminio Flamini |

Series | The Springer International Series in Engineering and Computer Science -- 680, International series in engineering and computer science -- 680. |

Contributions | Flamini, Flaminio |

Classifications | |
---|---|

LC Classifications | TK1-9971 |

The Physical Object | |

Format | [electronic resource] / |

Pagination | 1 online resource (x, 176 pages). |

Number of Pages | 176 |

ID Numbers | |

Open Library | OL27038808M |

ISBN 10 | 1461353238, 1461509572 |

ISBN 10 | 9781461353232, 9781461509578 |

OCLC/WorldCa | 852792579 |

Commutative rings 13 1. Fixing terminology 13 2. Adjoining elements 16 3. Ideals and quotient rings 17 Rings of Finite Rank Chapter Structure of overrings 1. Introducing overrings they need, or are told they need, to learn some commutative algebra for their study of other subjects. Indeed, commutative algebra has come to File Size: 1MB.

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Finite Commutative Rings and Their Applications (The Springer International Series in Engineering and Computer Science Book ) - Kindle edition by Finite Commutative Rings and Their Applications book, Gilberto, Flamini, Flaminio.

Download it once and read it on your Kindle device, PC, phones or tablets. Use features like bookmarks, note taking and highlighting while reading Finite Commutative Rings and Their Author: Gilberto Bini, Flaminio Flamini. Finite Commutative Rings and their Applications answers a need for an introductory reference in finite commutative ring theory as applied to information and communication theory.

This book will be of interest to both professional and academic researchers in Format: Paperback. Finite Commutative Rings and their Applications is the first to address both theoretical and practical aspects of finite ring theory.

The authors provide a practical approach to finite rings through explanatory examples, thereby avoiding an abstract presentation Finite Commutative Rings and Their Applications book the subject. Foreword by Dieter Jungnickel Finite Commutative Rings and their Applications answers a need for an introductory reference in finite commutative ring theory as applied to information and.

Get this from a library. Finite commutative rings and their applications. [Gilberto Bini; Flaminio Flamini] -- This is a self-contained introductory reference to finite commutative ring theory as applied to information and communication theory.

Finite Commutative Rings and their Applications answers a need for an introductory reference in finite commutative ring theory as applied to information and communication theory. This book will be of interest to both professional and academic researchers in the fields of communication and coding theory.

Foreword by Dieter Jungnickel Finite Commutative Rings and their Applications answers a need for an introductory reference in finite commutative ring theory as applied to information and communication theory. This book will be of interest to both professional and academic researchers in the fields of communication and coding theory.

The book is a concrete and self. In mathematics, more specifically abstract algebra, a finite ring is a ring that has a finite number of elements.

Every finite field is an example of a finite ring, and the additive part of every finite ring is an example of an abelian finite group, but the concept of finite rings in their own right has a more recent history.

Although rings have more structure than groups, the theory of. Is there a classification of finite commutative rings available. If not, what are the best structure theorem that are known at present.

All I know is a result that every finite commutative ring is a direct product of local commutative rings (this is correct, right?) in some paper which computes the size of the general linear group over that ring.

Finite Commutative Rings and their Applicationsanswers a need for an introductory reference in finite commutative ring theory as applied to information and communication theory. This book will be of interest to both professional and academic researchers in.

Foreword by Dieter Jungnickel Finite Commutative Rings and their Applications answers a need for an introductory reference in finite commutative ring theory as applied to information and communication theory.

This book will be of interest to both professional and academic researchers in the fields of communication and coding theory. Finite Commutative Rings and Their Applications. Book June Finite Commutative Rings and Their Applications | Foreword by Dieter Jungnickel Finite Commutative Rings and their Applications answers a need for an introductory reference in finite commutative ring theory as applied to information and communication theory.

Commutative rings, together with ring homomorphisms, form a category. The ring Z is the initial object in this category, which means that for any commutative ring R, there is a unique ring homomorphism Z → R.

By means of this map, an integer n can be regarded as an element of R. For example, the binomial formula. Examples. Splitting Rings 75 6 GALOIS AND QUASI-GALOIS RINGS: STRUCTURE AND PROPERTIES 81 Classical Constructions 82 Galois Ring Properties 92 Structure Theorems for finite commutative local rings.

Another class of finite commutative local rings: Quasi-Galois Rings 7 BASIC NOTIONS ON CODES OVER FINITE FIELDS Stack Exchange network consists of Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers.

(Think about the form of ideals in finite direct products of rings.). This book provides an introduction to the basics and recent developments of commutative algebra. A glance at the contents of the first five chapters shows that the topics covered are ones that usually are included in any commutative algebra text.

A commutative ring with identity is called a chain ring if all its ideals form a chain under inclusion. A finite chain ring, roughly speaking, is an extension over a Galois ring of characteristic p n using an Eisenstein polynomial of degree p∤k, such rings were classified up to isomorphism by Clark and r, relatively little is known about finite chain rings when p∣ by: Cite this chapter as: Bini G., Flamini F.

() Finite Commutative Rings. Regular Polynomials. In: Finite Commutative Rings and Their : Gilberto Bini, Flaminio Flamini. Foreword by Dieter Jungnickel \ud Finite Commutative Rings and their Applications answers a need for an introductory reference in finite commutative ring theory as applied to information and communication theory.

This book will be of interest to both professional and academic researchers in the fields of communication and coding theory.\ud \ud Author: G Bini and F Flamini. Don't tell me about finite division rings or Boolean rings being commutative, or applications of their commutativity.

The proofs of their commutativity does not need the generality of. Publisher Summary. This chapter discusses the algebras with Hochschild dimension ≤ 1. It is assumed that A is algebra over a commutative ring is supposed that A 0 is the opposite K-algebra to A, and A ® A 0 is their tensor product over K, the enveloping algebra of A.

A can be regarded as a left A ® A 0-module in the natural homological dimension of this. This is an old question, but I recently came across this result and used it repeatedly before realizing that it is actually false.

This is inconvenient, so in the interest of preventing this from happening to other people, I will post an answer. "This book offers a comprehensive and thorough presentation of crucial research of the field of algebraic coding theory over finite commutative rings, particularly over finite Frobenius rings.

It is also a good guide to the literature on the subject. 4/5(1). Let R be a commutative ring with identity and let Z (R) be the set of zero-divisors of R. The essential graph of R is defined as the graph EG (R) with the vertex set Z (R) ∗ = Z (R) \ { 0 }, and two distinct vertices x and y are adjacent if and only if ann R (x y) is an essential by: 1.

abelian categories with applications to rings and modules Download abelian categories with applications to rings and modules or read online books in PDF, EPUB, Tuebl, and Mobi Format.

Click Download or Read Online button to get abelian categories with applications to rings and modules book now. This site is like a library, Use search box in the.

Note: If you're looking for a free download links of Commutative Algebra: Constructive Methods: Finite Projective Modules (Algebra and Applications) Pdf, epub, docx and torrent then this site is not for you.

only do ebook promotions online and we does not distribute any free download of ebook on this site. A Characterization of Finite Commutati ve Rings Roger A lperin and E loise H amann W e give a partial con verse to the w ell-kno wn result: ÔIf R is Þ nite commuta-tive ring with identity then every element is a unit or a zero divisorÕ.

An important partial con verse of this which we use here is that: ÔA Þ eld which is Þ nitely gen. A ring is called commutative if its multiplication is ative rings resemble familiar number systems, and various definitions for commutative rings are designed to formalize properties of the ative rings are also important in algebraic commutative ring theory, numbers are often replaced by ideals, and the definition of the prime.

Subjects Primary: 12C05 12C30 16A44 Secondary: 13B Galois theory 13B Polynomials over commutative rings [See also 11C08, 11T06, 13F20, 13M10] Keywords Finite commutative rings finite local rings Galois theory finite fields.

Citation. The first book on commutative semigroups was Redei's The theory ly generated commutative semigroups, published in Budapest in Subsequent years have brought much progress. By the structure of finite commutative semigroups was fairly well understood.

Recent results have perfected this understanding and extended it to finitely. MATHEMATICS MAGAZINE COROLLARY1. If p is a prime there are, up to isomorphism, exactly two rings of order p, namely Z, and C,(O). COROLLARY2. If p and q are distinct primes there are, up to isomorphism, exactly four rings of order pq.

These are Z, C,(O), C,(O) +Z, and Z, +C,(O). More generally if n is a square-free positive integer and R is a ring of order n,File Size: KB. Subgroups. Sylow’s Theorem. Decomposition Theorem for Finite Abelian Groups.

Chapter17 Rings: Definitions and Elementary Properties Commutative Rings. Unity. Invertibles and Zero-Divisors. Integral Domain. Field. Chapter18 Ideals and Homomorphisms Chapter19 Quotient Rings Construction of Quotient Rings.

Examples. Fundamental Homomorphism. The book presents in a unified manner the more fundamental aspects of finite groups and their applications, and at the same time preserves the advantage which arises when each branch of an extensive subject is written by a specialist in that branch.

( views) An Introduction to Group Theory: Applications to Mathematical Music Theory. Their main interests may be in other areas of mathematics, such as combinatorics, topology, number theory, commutative algebra, and so on. These students need a solid, comprehensive grounding in representation theory that enables them to apply the theory to their own situation as the occasion demands.

They need to be able toFile Size: 1MB. A Term of Commutative Algebra. This book is a clear, concise, and efficient textbook, aimed at beginners, with a good selection of topics. Topics covered includes: Rings and Ideals, Radicals, Filtered Direct Limits, Cayley–Hamilton Theorem, Localization of Rings and Modules, Krull–Cohen–Seidenberg Theory, Rings and Ideals, Direct Limits, Filtered direct limit.

Firstly, what’s a ring. One of the definitions is as follows. A ring [math](R,+.)[/math] is a set [math]R[/math] together with two operations [math]+[/math] and. Find many great new & used options and get the best deals for Algebra and Applications: Foundations of Commutative Rings and Their Modules 22 by Fanggui Wang and Hwankoo Kim (, Hardcover) at the best online prices at eBay.

Free shipping for many products. Often we get a classifying topos by taking a finite limits theory T T and forming the category of presheaves T ^ = Set T op \hat{T} = Set^{T^{op}}.For example, in their book, Mac Lane and Moerdijk get the classifying topos for commutative rings.

Commutative algebra Author. Quitté, Claude; Series. Algebras and applications ; v. [More in this series] Algebra and applications, ; volume 20 ; Summary note Translated from the popular French edition, this book offers a detailed introduction to various basic concepts, methods, principles, and results of commutative algebra.

The study of the prime and primitive ideal spectra of various classes of rings forms a common theme in the lectures, and they touch on such topics as the structure of group rings of polycyclic-by-finite groups, localization in non commutative rings, and rings of differential operators.Featuring presentations from the Fourth International Conference on Commutative Algebra held in Fez, Morocco, this reference presents trends in the growing area of commutative algebra.

With contributions from nearly 50 internationally renowned researchers, the book emphasizes innovative applications and connections to algebraic number theory.Dougherty S, Kim J, Kulosman H and Liu H () Self-dual codes over commutative Frobenius rings, Finite Fields and Their Applications,(), Online publication date: 1-Jan Ilten N and Süβ H () Algebraic geometry codes from polyhedral divisors, Journal of Symbolic Computation,(), Online publication date: 1.