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| Author | : Alberto Corso |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 233 |
| Release | : 2011-10-20 |
| Genre | : Mathematics |
| ISBN | : 082184959X |
Download Commutative Algebra and Its Connections to Geometry Book in PDF, ePub and Kindle
This volume contains papers based on presentations given at the Pan-American Advanced Studies Institute (PASI) on commutative algebra and its connections to geometry, which was held August 3-14, 2009, at the Universidade Federal de Pernambuco in Olinda, Brazil. The main goal of the program was to detail recent developments in commutative algebra and interactions with such areas as algebraic geometry, combinatorics and computer algebra. The articles in this volume concentrate on topics central to modern commutative algebra: the homological conjectures, problems in positive and mixed characteristic, tight closure and its interaction with birational geometry, integral dependence and blowup algebras, equisingularity theory, Hilbert functions and multiplicities, combinatorial commutative algebra, Grobner bases and computational algebra.
| Author | : David Eisenbud |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 784 |
| Release | : 2013-12-01 |
| Genre | : Mathematics |
| ISBN | : 1461253500 |
Download Commutative Algebra Book in PDF, ePub and Kindle
This is a comprehensive review of commutative algebra, from localization and primary decomposition through dimension theory, homological methods, free resolutions and duality, emphasizing the origins of the ideas and their connections with other parts of mathematics. The book gives a concise treatment of Grobner basis theory and the constructive methods in commutative algebra and algebraic geometry that flow from it. Many exercises included.
| Author | : Jean-Pierre Serre |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 139 |
| Release | : 2012-12-06 |
| Genre | : Mathematics |
| ISBN | : 3662042037 |
Download Local Algebra Book in PDF, ePub and Kindle
This is an English translation of the now classic "Algbre Locale - Multiplicits" originally published by Springer as LNM 11. It gives a short account of the main theorems of commutative algebra, with emphasis on modules, homological methods and intersection multiplicities. Many modifications to the original French text have been made for this English edition, making the text easier to read, without changing its intended informal character.
| Author | : Ernst Kunz |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 253 |
| Release | : 2012-11-06 |
| Genre | : Mathematics |
| ISBN | : 1461459877 |
Download Introduction to Commutative Algebra and Algebraic Geometry Book in PDF, ePub and Kindle
Originally published in 1985, this classic textbook is an English translation of Einführung in die kommutative Algebra und algebraische Geometrie. As part of the Modern Birkhäuser Classics series, the publisher is proud to make Introduction to Commutative Algebra and Algebraic Geometry available to a wider audience. Aimed at students who have taken a basic course in algebra, the goal of the text is to present important results concerning the representation of algebraic varieties as intersections of the least possible number of hypersurfaces and—a closely related problem—with the most economical generation of ideals in Noetherian rings. Along the way, one encounters many basic concepts of commutative algebra and algebraic geometry and proves many facts which can then serve as a basic stock for a deeper study of these subjects.
| Author | : Susan M. Cooper |
| Publisher | : Springer |
| Total Pages | : 328 |
| Release | : 2014-05-16 |
| Genre | : Mathematics |
| ISBN | : 1493906267 |
Download Connections Between Algebra, Combinatorics, and Geometry Book in PDF, ePub and Kindle
Commutative algebra, combinatorics, and algebraic geometry are thriving areas of mathematical research with a rich history of interaction. Connections Between Algebra and Geometry contains lecture notes, along with exercises and solutions, from the Workshop on Connections Between Algebra and Geometry held at the University of Regina from May 29-June 1, 2012. It also contains research and survey papers from academics invited to participate in the companion Special Session on Interactions Between Algebraic Geometry and Commutative Algebra, which was part of the CMS Summer Meeting at the University of Regina held June 2–3, 2012, and the meeting Further Connections Between Algebra and Geometry, which was held at the North Dakota State University February 23, 2013. This volume highlights three mini-courses in the areas of commutative algebra and algebraic geometry: differential graded commutative algebra, secant varieties, and fat points and symbolic powers. It will serve as a useful resource for graduate students and researchers who wish to expand their knowledge of commutative algebra, algebraic geometry, combinatorics, and the intricacies of their intersection.
| Author | : Michael F. Atiyah |
| Publisher | : CRC Press |
| Total Pages | : 140 |
| Release | : 2018-03-09 |
| Genre | : Mathematics |
| ISBN | : 0429973268 |
Download Introduction To Commutative Algebra Book in PDF, ePub and Kindle
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. Keith Dennis |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 250 |
| Release | : 1992 |
| Genre | : Mathematics |
| ISBN | : 0821851306 |
Download Algebraic $K$-Theory, Commutative Algebra, and Algebraic Geometry Book in PDF, ePub and Kindle
In the mid-1960's, several Italian mathematicians began to study the connections between classical arguments in commutative algebra and algebraic geometry, and the contemporaneous development of algebraic K-theory in the US. These connections were exemplified by the work of Andreotti-Bombieri, Salmon, and Traverso on seminormality, and by Bass-Murthy on the Picard groups of polynomial rings. Interactions proceeded far beyond this initial point to encompass Chow groups of singular varieties, complete intersections, and applications of K-theory to arithmetic and real geometry. This volume contains the proceedings from a US-Italy Joint Summer Seminar, which focused on this circle of ideas. The conference, held in June 1989 in Santa Margherita Ligure, Italy, was supported jointly by the Consiglio Nazionale delle Ricerche and the National Science Foundation. The book contains contributions from some of the leading experts in this area.
| Author | : Gert-Martin Greuel |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 703 |
| Release | : 2007-11-05 |
| Genre | : Mathematics |
| ISBN | : 3540735410 |
Download A Singular Introduction to Commutative Algebra Book in PDF, ePub and Kindle
This substantially enlarged second edition aims to lead a further stage in the computational revolution in commutative algebra. This is the first handbook/tutorial to extensively deal with SINGULAR. Among the book’s most distinctive features is a new, completely unified treatment of the global and local theories. Another feature of the book is its breadth of coverage of theoretical topics in the portions of commutative algebra closest to algebraic geometry, with algorithmic treatments of almost every topic.
| Author | : Jurgen Herzog |
| Publisher | : CRC Press |
| Total Pages | : 424 |
| Release | : 2001-03-06 |
| Genre | : Mathematics |
| ISBN | : 9780203908013 |
Download Geometric And Combinatorial Aspects Of Commutative Algebra Book in PDF, ePub and Kindle
This work is based on the lectures presented at the International Conference of Commutative Algebra and Algebraic Geometry held in Messina, Italy. It discusses developments and advances in commutative algebra, algebraic geometry, and combinatorics - highlighting the theory of projective schemes, the geometry of curves, determinantal and stable idea
| Author | : Miles Reid |
| Publisher | : Cambridge University Press |
| Total Pages | : 172 |
| Release | : 1995-11-30 |
| Genre | : Mathematics |
| ISBN | : 9780521458894 |
Download Undergraduate Commutative Algebra Book in PDF, ePub and Kindle
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.
