TY  - BOOK
AU  - 
AU  - 
AU  - 
ED  - SpringerLink (Online service)
TI  - Monomial Ideals, Computations and Applications
T2  - Lecture Notes in Mathematics,
SN  - 9783642387425
AV  -  Libro electrónico 
U1  - 512 23
PY  - 2013///
CY  - Berlin, Heidelberg
PB  - Springer Berlin Heidelberg, Imprint: Springer
KW  - Mathematics
KW  - Algebra
N1  - A survey on Stanley depth -- Stanley decompositions using CoCoA -- A beginners guide to edge and cover ideals -- Edge ideals using Macaulay2 -- Local cohomology modules supported on monomial ideals -- Local Cohomology using Macaulay2
N2  - This work covers three important aspects of monomials ideals in the three chapters "Stanley decompositions" by Jȭrgen 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, Grȵbner 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
UR  - http://dx.doi.org/10.1007/978-3-642-38742-5
ER  -