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

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## 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) |
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Uncontrolled Keywords: | Irreducible, Monomial, Commutative, Algebra, Stanley, Computing, Depth, Bounds, Monomial |

Subjects: | Physical Sciences (f) > Mathematics(f5) |

ID Code: | 7267 |

Deposited By: | Mr. Javed Memon |

Deposited On: | 26 Dec 2011 14:02 |

Last Modified: | 26 Dec 2011 14:02 |

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