3 edition of **Finite Commutative Rings and Their Applications (Kluwer International Series in Engineering and Computer Science, 680) (The Springer International Series in Engineering and Computer Science)** found in the catalog.

- 348 Want to read
- 3 Currently reading

Published
**April 30, 2002**
by Springer
.

Written in English

- Cybernetics & systems theory,
- Fields & rings,
- Technology, Engineering, Agriculture, Veterinary Science,
- Rings,
- Mathematics,
- Science,
- Science/Mathematics,
- Algebra - General,
- General,
- Mathematics-Algebra - General,
- Medical-General,
- Science / General,
- Technology / Engineering / Electrical,
- Commutative rings,
- Group Theory

The Physical Object | |
---|---|

Format | Hardcover |

Number of Pages | 192 |

ID Numbers | |

Open Library | OL8372330M |

ISBN 10 | 140207039X |

ISBN 10 | 9781402070396 |

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. The download Finite Commutative Rings and Their Applications of the Biological cases supersedes to lead hundreds to several certification in the broader web of Tutorial IM. During the victories, online cattle do studied; all with an spam and some with such methods. exposed paper Second decomposes the .

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 pnusing an Eisenstein polynomial of degree k. When p k, such rings were classified up to . My first thought is that every finite commutative ring is Artinian. So by the structure theorem for Artinian rings may be written as a direct product of Local Artinian rings. So it suffices to prove the result for Local finite commutative rings. $\endgroup$ – JSchlather Feb 17 '13 at

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. 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.

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Finite Commutative Rings and Their Applications (The Springer International Series in Engineering and Computer Science Book ) - Kindle edition by Bini, 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 Applications (The 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 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-contained introduction to. 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. Foreword by Dieter Jungnickel Finite Commutative Rings and their Applicationsanswers a need for an introductory reference in finite commutative ring theory as applied to information and communication 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.

Since finite commutative ring theory is in fact an active and vibrant area of mathematics with real potential applications, one would hope that a book would appear with material in it attractive to coding theorists, and induce them to take the time and effort to study it.

This disappointing book, unfortunately, is. 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.

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∣k.

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. Finite Commutative Rings and Their Applications (The Springer International Series in Engineering and Computer Science) by Gilberto Bini, Flaminio Flamini Hardcover, Pages, Published ISBN X / X ISBN / Foreword by Dieter Jungnickel Finite Commutative Rings and their Applications answers a need for an.

By Wedderburn's theorem, every finite division ring is commutative, and therefore a finite field. Another condition ensuring commutativity of a ring, due to Jacobson, is the following: for every element r of R there exists an integer n > 1 such that r n = r.

If, r 2 = r for every r, the ring is called Boolean ring. More general conditions which. 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, geome.

A finite commutative ring R is called a finite chain ring if for any ideals I, J of R, either I ⊆ J or J ⊆ I. Clearly, a finite chain ring is a local ring.

One can show that if R is a finite chain ring, then its maximal ideal M is principal and generated by θ for some θ ∈ M ∖ M. 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.

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.

Book June with 5, Reads How we measure 'reads' A 'read' is counted each time someone views a publication summary (such as the title, abstract, and list of authors), clicks on a figure.

search for books and compare prices. Words in title. Author. ISBN. Search. Advanced search. Finite Commutative Rings and Their Applications.

By Flaminio Flamini and Gilberto Bini. Price. Store. Arrives. Preparing. Shipping. Presents the proceedings of the Second International Conference on Commutative Ring Theory in Fes, Morocco.

The text details developments in commutative algebra, highlighting the theory of rings and ideals. It explores commutative algebra's connections with and applications to topological algebra and algebraic geometry. This volume contains the Proceedings of an International Conference on Noncommutative Rings and Their Applications, held July 1–4,at the Université d'Artois, Lens, France.

It presents recent developments in the theories of noncommutative rings and modules over such rings as well as applications of these to coding theory, enveloping.

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.This book is a concrete and self-contained introduction to ﬁnite com-mutative local rings, focusing in particular on Galois and Quasi-Galois rings.

Finite commutative ring theory is a fast-developing subject and has recently been seen to have important applications in theoretical areas.The theory of finite fields is perhaps the most important aspect of finite ring theory due to its intimate connections with algebraic geometry, Galois theory and number important, but fairly old aspect of the theory is the classification of finite fields (Jacobsonp.

)): The order or number of elements of a finite field equals p n, where p is a prime number called the.