# Monomial Ideals, Computations and Applications

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This work covers three important aspects of monomials ideals in the three chapters qStanley decompositionsq by JA¼rgen Herzog, qEdge idealsq by Adam Van Tuyl and qLocal cohomologyq by Josep A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, GrApbner 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.of I with respect to i to be the monomial ideal J D .v1;:::;v m/ SAy, where y is an indeterminate over S and y.uj=xi/; if x2 i divides uj ; vj ... However if we drop the assumption that dim K M a A 1 for all a, an answer to Question 65 seems to be hard.

 Title : Monomial Ideals, Computations and Applications Author : Anna Maria Bigatti, Philippe Gimenez, Eduardo Sáenz-de-Cabezón Publisher : Springer - 2013-08-24