Monomial ideals, computations and applications Anna M. Bigatti, Philippe Gimenez, Eduardo Sáenz-de-Cabezón, editors

Format:

Book

Contributor:

Bigatti, Anna M. (Anna Maria), 1965-

Gimenez, Philippe

Sáenz-de-Cabezón, Eduardo

Series:

Lecture notes in mathematics (Springer-Verlag) ; 0075-8434 2083

Lecture notes in mathematics 1617-9692 2083

Language:

English

Subjects (All):

Commutative algebra.

Ideals (Algebra).

Physical Description:

1 online resource

Place of Publication:

Heidelberg Springer ©2013

Language Note:

English

System Details:

text file

PDF

Summary:

This work covers three important aspects of monomials ideals in the three chapters "Stanley decompositions" by Jrgen Herzog, "Edge ideals" by Adam Van Tuyl and "Local cohomology" by Josep lvarez Montaner. The chapters, written by top experts, include computer tutorials that emphasize the computational aspects of the respective areas. Monomial ideals and algebras are, in a sense, among the simplest structures in commutative algebra and the main objects of combinatorial commutative algebra. Also, they are of major importance for at least three reasons. Firstly, Grbner basis theory allows us to treat certain problems on general polynomial ideals by means of monomial ideals. Secondly, the combinatorial structure of monomial ideals connects them to other combinatorial structures and allows us to solve problems on both sides of this correspondence using the techniques of each of the respective areas. And thirdly, the combinatorial nature of monomial ideals also makes them particularly well suited to the development of algorithms to work with them and then generate algorithms for more general structures

Contents:

Part I: Stanley Decompositions. A Survey on Stanley Depth Jürgen Herzog Stanley Decompositions Using CoCoA Anna Maria Bigatti, Emanuela De Negri

Part II: Edge Ideals. A Beginner's Guide to Edge and Cover Ideals Adam Van Tuyl Edge Ideals Using Macaulay2 Adam Van Tuyl

Part III: Local Cohomology. Local Cohomology Modules Supported on Monomial Ideals Josep Àlvarez Montaner Local Cohomology Using Macaulay2 Josep Àlvarez Montaner, Oscar Fernández-Ramos

Notes:

Includes bibliographical references (pages 187-194)

Online resource; title from PDF title page (SpringerLink, viewed August 28, 2013)

Other Format:

Print version Monomial ideals, computations and applications

ISBN:

9783642387425

364238742X

OCLC:

857119525

Access Restriction:

Restricted for use by site license