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Graded Syzygies [electronic resource] / by Irena Peeva.

By: Peeva, Irena [author.].
Contributor(s): SpringerLink (Online service).
Material type: materialTypeLabelBookSeries: Algebra and Applications: 14Publisher: London : Springer London, 2011Description: XII, 304 p. online resource.Content type: text Media type: computer Carrier type: online resourceISBN: 9780857291776.Subject(s): Mathematics | Algebra | Mathematics | Commutative Rings and AlgebrasDDC classification: 512.44 Online resources: Click here to access online
Contents:
Graded Free Resolutions -- Hilbert Functions -- Monomial Resolutions -- Syzygies of Toric Ideals.
In: Springer eBooksSummary: The study of free resolutions is a core and beautiful area in Commutative Algebra. The main goal of this book is to inspire the readers and develop their intuition about syzygies and Hilbert functions. Many examples are given in order to illustrate ideas and key concepts. A valuable feature of the book is the inclusion of open problems and conjectures; these provide a glimpse of exciting, and often challenging, research directions in the field. Three types of problems are presented: Conjectures, Problems, and Open-Ended Problems. The latter do not describe specific problems but point to interesting directions for exploration. The first part of the monograph contains basic background material on graded free resolutions. Further coverage of topics includes syzygies over a polynomial ring, resolutions  over quotient rings, lex ideals and Hilbert functions, compression, resolutions of monomial ideals, and syzygies of toric ideals. With a clear and self-contained exposition this text is intended for advanced graduate students and postdoctorates; it will be also of interest to senior mathematicians.
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Graded Free Resolutions -- Hilbert Functions -- Monomial Resolutions -- Syzygies of Toric Ideals.

The study of free resolutions is a core and beautiful area in Commutative Algebra. The main goal of this book is to inspire the readers and develop their intuition about syzygies and Hilbert functions. Many examples are given in order to illustrate ideas and key concepts. A valuable feature of the book is the inclusion of open problems and conjectures; these provide a glimpse of exciting, and often challenging, research directions in the field. Three types of problems are presented: Conjectures, Problems, and Open-Ended Problems. The latter do not describe specific problems but point to interesting directions for exploration. The first part of the monograph contains basic background material on graded free resolutions. Further coverage of topics includes syzygies over a polynomial ring, resolutions  over quotient rings, lex ideals and Hilbert functions, compression, resolutions of monomial ideals, and syzygies of toric ideals. With a clear and self-contained exposition this text is intended for advanced graduate students and postdoctorates; it will be also of interest to senior mathematicians.

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