# e-Book Graded Syzygies (Algebra and Applications) epub download

**Author:**Irena Peeva

**ISBN:**0857291769

**Pages:**304 pages

**Publisher:**Springer; 2011 edition (December 10, 2010)

**Language:**English

**Category:**Mathematics

**Size ePUB:**1925 kb

**Size Fb2:**1984 kb

**Size DJVU:**1822 kb

**Rating:**4.5

**Votes:**853

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**Subcategory:**Science

# e-Book Graded Syzygies (Algebra and Applications) epub download

#### by **Irena Peeva**

Algebra and Applications. Authors: Peeva, Irena. The main goal of this book is to inspire the readers and develop their intuition about syzygies and Hilbert functions.

Algebra and Applications. Focuses on the graded aspect of syzygies, while most of the standard texts in commutative algebra consider local rings. Provides a substantial amount of open problems and conjectures. Includes a wealth of examples.

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

The study of free resolutions is a core and beautiful area in Commutative Algebra. Three types of problems are presented: Conjectures, Problems, and Open-Ended Problems.

Автор: Irena Peeva Название: Graded Syzygies Издательство: Springer Классификация: ISBN . The theory developed within this book has potential applications in various branches of algebra, including homological algebra, ring theory and K-theory.

The theory developed within this book has potential applications in various branches of algebra, including homological algebra, ring theory and K-theory.

Irena Vassileva Peeva is a professor of mathematics at Cornell University, specializing in commutative algebra. She disproved the Eisenbud–Goto regularity conjecture jointly with Jason McCullough. Peeva did her graduate studies at Brandeis University, earning a P. in 1995 under the supervision of David Eisenbud with a thesis entitled Free Resolutions

Irena Peeva, Graded syzygies, Algebra and Applications, vol. 14, Springer-Verlag, 2011. We develop the basic theory quite generally, with a view toward future applications to a wide class of graded modules over graded rings.

Irena Peeva, Graded syzygies, Algebra and Applications, vol. The main application in this paper is to study the Betti poset B B(I,k) of a monomial ideal I in the polynomial ring R k over a field k, which consists of all degrees in Z^m of the homogeneous basis elements of the free modules in the minimal free Z^m-graded resolution of I over.

Irena Vassileva Peeva is a professor of mathematics at Cornell University, and the author of the book Graded Syzygies. Peeva did her graduate studies at Brandeis University, earning a Doctor of Philosophy in 1995 under the supervision of David Eisenbud with a thesis entitled Free Resolutions. In 2014 she was elected as a fellow of the American Mathematical Society "for contributions to commutative algebra and its applications. American Mathematical Society.

Irena Vassileva Peeva is a professor of mathematics at Cornell University, and the author of the book Graded Syzygies (Springer, 2011). for contributions to commutative algebra and its applications. in 1995 under the supervision of David Eisenbud with a thesis entitled Free Resolutions. In 2014 she was elected as a fellow of the American Mathematical Society.

Address: Department of Mathematics. Despite all this work on applications, progress on the structure of minimal free resolutions over complete intersections was scant

Address: Department of Mathematics. Syzygies and Hilbert functions, Lect. Despite all this work on applications, progress on the structure of minimal free resolutions over complete intersections was scant. The condition of minimality is important. The mere existence of free resolutions suffices for foundational issues such as the definition of Ext and Tor, and there are various methods of producing resolutions uniformly (for example, the Bar resolution).

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Syzygies and Hilbert Functions. Hilbert functions and resolutions are both central objects in commutative algebra and fruitful tools in the fields of algebraic geometry, combinatorics, commutative algebra, and computational algebra. Publisher: Chapman and Hall/CRC. Print ISBN: 9781138454316, 1138454311. Written by international mathematics authorities, the book first examines the invariant of Castelnuovo-Mumford regularity, blowup algebras, and bigraded rings.

<p>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.</p>

<p>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.</p>

<p>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.</p>