Author : Stephen McAdam
Publisher : American Mathematical Soc.
Page : 184 pages
File Size : 37,68 MB
Release : 1989
Category : Mathematics
ISBN : 082185108X
Discusses five closely related sets of prime ideals associated to an ideal I in a Noetherian ring, the persistent, asymptotic, quintasymptotic, essential, and quintessential primes of I. Requires a standard year course in commutative ring theory. Annotation copyright Book News, Inc. Portland, Or.
Author : Enrico Carlini
Publisher : Springer Nature
Page : 162 pages
File Size : 22,18 MB
Release : 2020-05-21
Category : Mathematics
ISBN : 3030452476
This book discusses regular powers and symbolic powers of ideals from three perspectives– algebra, combinatorics and geometry – and examines the interactions between them. It invites readers to explore the evolution of the set of associated primes of higher and higher powers of an ideal and explains the evolution of ideals associated with combinatorial objects like graphs or hypergraphs in terms of the original combinatorial objects. It also addresses similar questions concerning our understanding of the Castelnuovo-Mumford regularity of powers of combinatorially defined ideals in terms of the associated combinatorial data. From a more geometric point of view, the book considers how the relations between symbolic and regular powers can be interpreted in geometrical terms. Other topics covered include aspects of Waring type problems, symbolic powers of an ideal and their invariants (e.g., the Waldschmidt constant, the resurgence), and the persistence of associated primes.
Author : Craig Huneke
Publisher : Cambridge University Press
Page : 446 pages
File Size : 31,70 MB
Release : 2006-10-12
Category : Mathematics
ISBN : 0521688604
Ideal for graduate students and researchers, this book presents a unified treatment of the central notions of integral closure.
Author : Michael F. Atiyah
Publisher : CRC Press
Page : 140 pages
File Size : 27,89 MB
Release : 2018-03-09
Category : Mathematics
ISBN : 0429973268
First Published in 2018. This book grew out of a course of lectures given to third year undergraduates at Oxford University and it has the modest aim of producing a rapid introduction to the subject. It is designed to be read by students who have had a first elementary course in general algebra. On the other hand, it is not intended as a substitute for the more voluminous tracts such as Zariski-Samuel or Bourbaki. We have concentrated on certain central topics, and large areas, such as field theory, are not touched. In content we cover rather more ground than Northcott and our treatment is substantially different in that, following the modern trend, we put more emphasis on modules and localization.
Author : R. Y. Sharp
Publisher : Cambridge University Press
Page : 371 pages
File Size : 46,96 MB
Release : 2000
Category : Mathematics
ISBN : 0521646235
Introductory account of commutative algebra, aimed at students with a background in basic algebra.
Author : Miles Reid
Publisher : Cambridge University Press
Page : 172 pages
File Size : 50,49 MB
Release : 1995-11-30
Category : Mathematics
ISBN : 9780521458894
Commutative algebra is at the crossroads of algebra, number theory and algebraic geometry. This textbook is affordable and clearly illustrated, and is intended for advanced undergraduate or beginning graduate students with some previous experience of rings and fields. Alongside standard algebraic notions such as generators of modules and the ascending chain condition, the book develops in detail the geometric view of a commutative ring as the ring of functions on a space. The starting point is the Nullstellensatz, which provides a close link between the geometry of a variety V and the algebra of its coordinate ring A=k[V]; however, many of the geometric ideas arising from varieties apply also to fairly general rings. The final chapter relates the material of the book to more advanced topics in commutative algebra and algebraic geometry. It includes an account of some famous 'pathological' examples of Akizuki and Nagata, and a brief but thought-provoking essay on the changing position of abstract algebra in today's world.
Author : Ezra Miller
Publisher : Springer Science & Business Media
Page : 442 pages
File Size : 23,87 MB
Release : 2005-06-21
Category : Mathematics
ISBN : 9780387237077
Recent developments are covered Contains over 100 figures and 250 exercises Includes complete proofs
Author : Peter Buser
Publisher : Springer Science & Business Media
Page : 473 pages
File Size : 11,23 MB
Release : 2010-10-29
Category : Mathematics
ISBN : 0817649921
This monograph is a self-contained introduction to the geometry of Riemann Surfaces of constant curvature –1 and their length and eigenvalue spectra. It focuses on two subjects: the geometric theory of compact Riemann surfaces of genus greater than one, and the relationship of the Laplace operator with the geometry of such surfaces. Research workers and graduate students interested in compact Riemann surfaces will find here a number of useful tools and insights to apply to their investigations.
Author : Hideyuki Matsumura
Publisher : Cambridge University Press
Page : 338 pages
File Size : 33,90 MB
Release : 1989-05-25
Category : Mathematics
ISBN : 9780521367646
This book explores commutative ring theory, an important a foundation for algebraic geometry and complex analytical geometry.
Author : Winfried Bruns
Publisher : Springer
Page : 246 pages
File Size : 17,39 MB
Release : 2006-11-14
Category : Mathematics
ISBN : 3540392742
Determinantal rings and varieties have been a central topic of commutative algebra and algebraic geometry. Their study has attracted many prominent researchers and has motivated the creation of theories which may now be considered part of general commutative ring theory. The book gives a first coherent treatment of the structure of determinantal rings. The main approach is via the theory of algebras with straightening law. This approach suggest (and is simplified by) the simultaneous treatment of the Schubert subvarieties of Grassmannian. Other methods have not been neglected, however. Principal radical systems are discussed in detail, and one section is devoted to each of invariant and representation theory. While the book is primarily a research monograph, it serves also as a reference source and the reader requires only the basics of commutative algebra together with some supplementary material found in the appendix. The text may be useful for seminars following a course in commutative ring theory since a vast number of notions, results, and techniques can be illustrated significantly by applying them to determinantal rings.
