Progress in Commutative Algebra 2

Closures, Finiteness and Factorization
1. Auflage 2012
ISBN: 978-3-11-027859-0
Verlag: De Gruyter

Buch, Englisch, 315 Seiten, Format (B × H): 175 mm x 246 mm, Gewicht: 737 g

Reihe: De Gruyter Proceedings in Mathematics

This is the second of two volumes of a state-of-the-art survey article collection which originates from three commutative algebra sessions at the 2009 Fall Southeastern American Mathematical Society Meeting at Florida Atlantic University. The articles reach into diverse areas of commutative algebra and build a bridge between Noetherian and non-Noetherian commutative algebra. These volumes present current trends in two of the most active areas of commutative algebra: non-noetherian rings (factorization, ideal theory, integrality), and noetherian rings (the local theory, graded situation, and interactions with combinatorics and geometry).

This volume contains surveys on aspects of closure operations, finiteness conditions and factorization. Closure operations on ideals and modules are a bridge between noetherian and nonnoetherian commutative algebra. It contains a nice guide to closure operations by Epstein, but also contains an article on test ideals by Schwede and Tucker and one by Enescu which discusses the action of the Frobenius on finite dimensional vector spaces both of which are related to tight closure.

Finiteness properties of rings and modules or the lack of them come up in all aspects of commutative algebra. However, in the study of non-noetherian rings it is much easier to find a ring having a finite number of prime ideals. The editors have included papers by Boynton and Sather-Wagstaff and by Watkins that discuss the relationship of rings with finite Krull dimension and their finite extensions. Finiteness properties in commutative group rings are discussed in Glaz and Schwarz's paper. And Olberding's selection presents us with constructions that produce rings whose integral closure in their field of fractions is not finitely generated. The final three papers in this volume investigate factorization in a broad sense. The first paper by Celikbas and Eubanks-Turner discusses the partially ordered set of prime ideals of the projective line over the integers. The editors have also included a paper on zero divisor graphs by Coykendall, Sather-Wagstaff, Sheppardson and Spiroff. The final paper, by Chapman and Krause, concerns non-unique factorization.

Zielgruppe

Graduate and PhD Students, Researchers, Lecturers; Academic Libraries

Autoren/Hrsg.

Vassilev, Janet C.

Francisco, Christopher

Sather-Wagstaff, Sean M.

Klingler, Lee C.

Weitere Mitwirkende

Boynton, Jason G.

Celikbas, Ela

Chapman, Scott T.

Coykendall, Jim

Enescu, Florian

Epstein, Neil

Eubanks-Turner, Christina

Glaz, Sarah

Krause, Ulrich

Olberding, Bruce

Sather-Wagstaff, Sean

Schwarz, Ryan

Schwede, Karl

Sheppardson, Laura

Spiroff, Sandra

Tucker, Kevin

Watkins, John J.

Fachgebiete

• Mathematik | Informatik Mathematik Algebra
• Mathematik | Informatik Mathematik Geometrie Algebraische Geometrie

Inhaltsverzeichnis

Frontmatter
Preface
Contents
A Guide to Closure Operations in Commutative Algebra
A Survey of Test Ideals
Finite-dimensional Vector Spaces with Frobenius Action
Finiteness and Homological Conditions in Commutative Group Rings
Regular Pullbacks
Noetherian Rings without Finite Normalization
Krull Dimension of Polynomial and Power Series Rings
The Projective Line over the Integers
On Zero Divisor Graphs
A Closer Look at Non-Unique Factorization via Atomic Decay and Strong Atoms

Über Autor(innen)

Christopher Francisco, Oklahoma State University, Stillwater, Oklahoma, USA; Lee C. Klingler, Florida Atlantic University, Boca Raton, Florida, USA; Sean M. Sather-Wagstaff, North Dakota State University, Fargo, North Dakota, USA; Janet Vassilev, University of New Mexico, Albuquerque, New Mexico, USA.