# Computing the Stanley depth

Qureshi, Muhammad Imran (2011) Computing the Stanley depth. PhD thesis, Govt. College University, Lahore .

 HTML13Kb

## Abstract

In the first Chapter some definitions and necessary results from commutative algebra are given.Also some detail are given which leads us towards the Stanley decompositions of multigraded S-modules, where S = F[σ1, . . . , σn] is a polynomial ring in n variables over a field F. In the end of the chapter we give some important results about the Stanley decompositions and Stanley’s conjecture. In Chapter 2 for the given monomial primary ideals Ω and Ω′ of S, we gave an upper bound for the Stanley depth of S/(Ω ∩ Ω′) which is reached if Ω, Ω′ are irreducible. Also we showed that Stanley’s Conjecture holds for Ω1∩Ω2, S/(Ω1∩Ω2∩ Ω3), (Ωi)i being some irreducible monomial ideals of S. These results are published in our paper [23]. For integers 1 ≤ t < n consider the ideal I = (σ1, . . . , σt) ∩ (σt+1, . . . , σn) in S. In Chapter 3 we gave an upper bound for the Stanley depth of the ideal I′ = (I, σn+1, . . . , σn+p) ⊂ S′ = S[σn+1, . . . , σn+p]. We gave similar upper bounds for the Stanley depth of the ideal (In;2, σn+1, . . . , σn+p), where In;2 is the square free Veronese ideal of degree 2 in n variables. These results are from our paper [11].

Item Type: Thesis (PhD) Irreducible, Monomial, Commutative, Algebra, Stanley, Computing, Depth, Bounds, Monomial Physical Sciences (f) > Mathematics(f5) 7267 Mr. Javed Memon 26 Dec 2011 14:02 26 Dec 2011 14:02

Repository Staff Only: item control page