

Title of Thesis
CohenMacaulay Modifications of Square free Monomial Ideals 
Author(s)
Safyan Ahmad 
Institute/University/Department
Details Abdus Salam School of Mathematical Sciences / GC
University, Lahore 
Session 2010 
Subject Mathematics 
Number of Pages 57 
Keywords (Extracted from title, table of contents and
abstract of thesis) CohenMacaulay,
Modifications, Square free, Monomial, Ideals, intersections,
irreducible 
Abstract In this dissertation
we study Cohen–Macaulay monomial ideals with a given radical. Among
this set of ideals are the socalled Cohen–Macaulay modifications.
Not all Cohen–Macaulay squarefree monomial ideals admit nontrivial
Cohen–Macaulay modifications. It is shown that if there exists one
such modification, then there exist indeed infinitely many. We also
present classes of Cohen–Macaulay squarefree monomial ideals with
infinitely many nontrivial Cohen–Macaulay modifications.
We also study ideals which are the intersections of irreducible
monomial ideals of height 2, whose radical is Cohen–Macaulay. Such
ideals are naturally associated to a graph. For these ideals we give
sufficient conditions in terms of the graph to be Cohen–Macaulay..

