6 edition of **Modules over non-Noetherian domains** found in the catalog.

Modules over non-Noetherian domains

LГЎszlГі Fuchs

- 348 Want to read
- 10 Currently reading

Published
**2001**
by American Mathematical Society in Providence, RI
.

Written in English

- Modules (Algebra),
- Integral domains,
- Commutative rings

**Edition Notes**

Includes bibliographical references (p. 591-602) and indexes

Statement | László Fuchs, Luigi Salce |

Series | Mathematical surveys and monographs -- v. 84, Mathematical surveys and monographs -- no. 84 |

Contributions | Salce, Luigi |

Classifications | |
---|---|

LC Classifications | QA247 .F83 2001 |

The Physical Object | |

Pagination | xvi, 613 p. ; |

Number of Pages | 613 |

ID Numbers | |

Open Library | OL17008475M |

ISBN 10 | 0821819631 |

LC Control Number | 00044205 |

Module-like constructions Finite type and coherent sheaves Pleasant properties of ﬁnite type and coherent sheaves ⋆⋆ Coherent modules over non-Noetherian rings Chapter Line bundles: Invertible sheaves and divisors Some line bundles on projective space Line bundles and Weil. Información del artículo MODULES OVER NON-NOETHERIAN DOMAINS (Mathematical Surveys and Monographs 84) By LÁSZLÓ FUCHS and LUIGI SALCE: pp., US$, ISBN (American Mathematical Society, Providence, RI, ).

Example A vector space V over a eld kis artinian as a k-module if and only if it is nite-dimensional over k(in which case it is clearly noetherian as a k-module too!). The implication \(" is clear for dimension reasons seen in the preceding example. For the converse, suppose V is not nite-dimensional and let fe ig i2I be a basis. By in. EXAMPLES OF NON-NOETHERIAN DOMAINS INSIDE POWER SERIES RINGS WILLIAM HEINZER, CHRISTEL ROTTHAUS, AND SYLVIA WIEGAND Abstract. Given a power series ring R∗ over a Noetherian integral domain R and an intermediate ﬁeld L between R and the total quotient ring of R∗, the integral domain A= L∩R∗ often (but not always) inherits nice properties.

variable over R. If Pis a projective A-module of rank d+1 satisfying property (R), then E(A P) acts transitively on Um(A P). In particular P is cancellative. We generalize () for Prufer domain as follows (see ): Let Rbe a Prufer domain of dimension dand A= R[Y;f 1], where Y is a variable over Rand f2R[Y]. If P is a projective A-module of. On the existence of unimodular elements and cancellation of projective modules over noetherian and non-noetherian rings Article in Journal of Algebra November with 18 Reads.

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Modules over Non-Noetherian Domains About this Title. László Fuchs, Tulane University, New Orleans, LA and Luigi Salce, University of Padova, Padova, Italy. Publication: Mathematical Surveys and Monographs Publication Year Volume 84 ISBNs: Cited by: The authors concentrate on modules over valuation and Prufer domains, but also discuss Krull and Matlis domains, $h$-local, reflexive, and coherent domains.

The volume can serve as a standard. Modules over Non-Noetherian Domains In this book, the authors present both traditional and modern discoveries in the subject area, concentrating on advanced aspects of the topic.

Existing material is studied in detail, including finitely generated modules, projective and injective modules, and the theory of torsion and torsion-free modules.

ISBN: OCLC Number: Description: xvi, pages ; 27 cm. Contents: Commutative Domains and Their Modules --Generalities on domains --Fractional ideals --Integral dependence --Module categories --Lemmas on Hom and Ext --Lemmas on tensor and torsion products --Divisibility and relative divisibility --Pure submodules --The exchange property --Semilocal.

Book reviews. MODULES OVER NON‐NOETHERIAN DOMAINS (Mathematical Surveys and Monographs 84) R. Sharp. University of Sheffield.

Search for more papers by this author. Sharp. University of Sheffield. Search for more papers by this author. First published: 23 December Cited by: Destination page number Search scope Search Text Search scope Search Text.

Modules over Non-Noetherian Domains Mathematical Surveys and Monographs: : Fuchs, Laszlo, Salce, Luigi: Libros en idiomas extranjerosReviews: 1. Modules over Non-Noetherian Domains Laszlo Fuchs Luigi Sake American Mathematical Society.

Table of Contents Preface xi List of Symbols xv Chapter I. Commutative Domains and Their Modules 1. Generalities on domains 1 2. Fractional ideals 9 3. Integral dependence 16 4. Module categories 22 5. Lemmas on Horn and Ext However, a non-Noetherian ring can be a subring of a Noetherian ring.

Since any integral domain is a subring of a field, any integral domain that is not Noetherian provides an example. To give a less trivial example, The ring of rational functions generated by x and y/x n over a field k is a subring of the field k(x,y) in only two variables.

In the university library, I was looking at Modules over Non-Noetherian Domains by Fuchs and Salce and I couldn't really understand anything. I'm also looking at the "Questions that may already have your answer," but if they do, it's not in a way that I can understand.

This specific book Modules over Non-Noetherian Domains (Mathematical Surveys and Monographs) was bright colored and of course has pictures on there.

As we know that book Modules over Non-Noetherian Domains (Mathematical Surveys and Monographs) has many kinds or variety. Start from kids until youngsters. Modules over non-Noetherian domains Home ; Modules over non-Noetherian domains Author: László Fuchs; Luigi Salce.

12 If you own the copyright to this book and it is wrongfully on our website, we offer a simple DMCA procedure to remove your content. Genre/Form: Electronic books: Additional Physical Format: Print version: Fuchs, László. Modules over non-Noetherian domains. Providence, RI: American Mathematical.

[2] L. Fuchs, On divisible modules over Conference on Abelian groups and Modules in Udine–, CISM Courses and Lectures, Vienna A module is Artinian (respectively Noetherian) if and only if it is so over its ring of homotheties.

An inﬁnite direct sum of non-zero modules is neither Artinian nor Noetherian. A vector space is Artinian (respectively Noetherian) if and only if its dimension is ﬁnite. We now list some elementary facts about Artinian and Noetherian modules. Commutative algebra is a rapidly growing subject that is developing in many different directions.

This volume presents several of the most recent results from various areas related to both Noetherian and non-Noetherian commutative algebra. This volume contains a collection of invited survey.

Personally I learned a lot from Otto Endler's Valuation Theory and Zariski-Samuel, Commutative Algebra Vol. Moreover Robert Gilmer's book on Multiplicative Ideal Theory and Fuchs-Salce, Modules over valuation domains.

H $\endgroup$ – Hagen Oct 20 '10 at A noetherian ring is a Krull domain if and only if it is an integrally closed domain. In the non-noetherian setting, one has the following: A direct limit of integrally closed domains is an integrally closed domain. Modules over an integrally closed domain.

This section needs expansion. You. Right V-rings R with infinitely generated right socle SOC(RR) such that R/SOC(RR) is a division ring are characterized as those non-noetherian rings over which a cyclic right module is either non. Modules over Non-Noetherian Domains: Fuchs, Laszlo, Salce, Luigi: Books - 5/5(1).

a non Noetherian ring that is a Noetherian $\\Bbb Z$-module a Noetherian ring that is a non Noetherian $\\Bbb Z$-module I have no idea in 1, and I'm not sure if $\\mathbf{Q}$ is right for 2? Just after the solution of Serre's conjecture by Quillen and Suslin, work started to explore projective modules over a non-noetherian base ring R.

An early result of Brewer and Costa in asserts that if R is a ring of dimension zero, then any finitely generated projective module over R [X 1, X 2,X n] is extended from R.Find many great new & used options and get the best deals for Modules over Non-Noetherian Domains Mathematical Surveys & Monographs Fuchs HC at the best online prices at eBay!

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