Monomial ideals, computations and applications
 Language
 English.
 Imprint
 Heidelberg : Springer, c2013.
 Physical description
 xi, 194 p. : ill. ; 24 cm.
 Series
 Lecture notes in mathematics (SpringerVerlag) 2083.
Access
Available online

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QA3 .L28 V.2083

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QA3 .L28 V.2083
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Contributors
Contents/Summary
 Bibliography
 Includes bibliographical references.
 Contents

 A survey on Stanley depth
 Stanley decompositions using CoCoA
 A beginner's guide to edge and cover ideals
 Edge ideals using Macaulay2
 Local cohomology modules supported on monomial ideals
 Local cohomology using Macaulay2.
 Summary
 This work covers three important aspects of monomials ideals in the three chapters "Stanley decompositions" by Jürgen Herzog, "Edge ideals" by Adam Van Tuyl and "Local cohomology" by Josep Álvarez 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, Gröbner 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.
Subjects
Bibliographic information
 Publication date
 2013
 Responsibility
 Anna M. Bigatti, Philippe Gimenez, Eduardo SáenzdeCabezón, editors.
 Series
 Lecture notes in mathematics, 00758434 ; 2083
 Available in another form
 9783642387425 (online)
 (GyWOH)har130424713
 ISBN
 9783642387418
 3642387411