Thesis (Master)--İzmir Institute of Technology, İzmir, 2005 / Keywords:Supplemented modules, cofinitely supplemented modules, cofinitely amply supplemented modules, cofinitely amply weakly supplemented modules. Includes bibliographical references (leaves 23).

This dissertation investigates the interplay between properties of Ext modules and ascent of module structures along ring homomorphisms. First, we consider a flat local ring homomorphism ϕ: (R, [special characters omitted], k) → (S, [special characters omitted]S, k). We show that if M is a finitely generated R-module such that [special characters omitted](S, M) satisfies NAK (e.g. if [special characters omitted](S, M) is finitely generated over S) for i = 1,…, dimR( M), then [special characters omitted](S, M) = 0 for all i ≠ 0 and M has an S-module structure via ϕ. We also provide explicit computations of [special characters omitted](S, M) to indicate how large it can be when M does not have a compatible S-module structure. Next, we consider the properties of an R-module M that has a compatible S-module structure via the flat local ring homomorphism ϕ. Our results in this direction show that M cannot see the difference between the rings R and S. Specifically, many homological invariants of M are the same when computed over R and over S. Finally, we investigate these ideas in the non-local setting. We consider a faithfully flat ring homomorphism ϕ: R → S such that for all [special characters omitted] ∈ m-Spec R, the map R/[special characters omitted] → S/[special characters omitted]S is an isomorphism and the induced map ϕ*: Spec( S) → Spec(R) is such that ϕ*(m-Spec( S)) ⊆ m-Spec(R), and show that if M is a finitely generated R-module such that [special characters omitted](S, M) satisfies NAK for i = 1,…,dim R(M), then M has an S-module structure via ϕ, and obtain the same Ext vanishing as in the local case.

by Leung Yiu-chung. / Thesis (M.Phil.)--Chinese University of Hong Kong, 1994. / Includes bibliographical references (leaves 79-81). / Introduction / Chapter 1 --- Preliminaries --- p.1 / Chapter 1.1 --- Chain Conditions --- p.4 / Chapter 1.2 --- Categories of Modules --- p.5 / Chapter 1.3 --- Projectivity and Injectivity --- p.5 / Chapter 2 --- Generalization on CS modules --- p.11 / Chapter 2.1 --- Introduction --- p.11 / Chapter 2.2 --- Preliminaries --- p.12 / Chapter 2.3 --- CS ring ´ؤ A generalization of injectivity --- p.16 / Chapter 2.4 --- GCS ring ´ؤ A further generalization of CS ring --- p.19 / Chapter 2.5 --- Generalized CS-modules --- p.24 / Chapter 2.5.1 --- Direct Sum of Uniform Modules --- p.25 / Chapter 2.5.2 --- GCS modules as direct sum of uniform modules --- p.28 / Chapter 3 --- Ascending Chain Condition on Essential Submodules --- p.35 / Chapter 3.1 --- Introduction --- p.35 / Chapter 3.2 --- Preliminaries --- p.36 / Chapter 3.3 --- Continuous rings with ACC on essential ideals --- p.38 / Chapter 3.4 --- Analogous Results On CS-modules --- p.44 / Chapter 3.5 --- Weak CS -modules --- p.50 / Chapter 3.5.1 --- Decomposition of Weak CS-modules --- p.53 / Chapter 3.6 --- Generalization of GCS-modules --- p.54 / Chapter 3.7 --- On CESS-modules --- p.57 / Chapter 3.7.1 --- On the decomposition of CESS-modules --- p.59 / Chapter 4 --- Non-Singular Rings --- p.63 / Chapter 4.1 --- CS-modules and CS-endomorphism rings --- p.63 / Chapter 4.2 --- Categorical Equivalence and Morita Equivalence --- p.70 / Chapter 4.3 --- Categories of CS-modules --- p.74 / Bibliography --- p.79

by Chui Chee Ping. / Thesis (M.Ph.)--Chinese University of Hong Kong, 1987. / Bibliograhph: leaves 47-49.

Thesis (M. Sc.)--University of Alberta, 2009. / Title from pdf file main screen (viewed on Dec. 10, 2009). "A thesis submitted to the Faculty of Graduate Studies and Research in partial fulfillment of the requirements for the degree of Master of Science in Pure Mathematics, Department of Mathematical and Statistical Sciences, University of Alberta." Includes bibliographical references.

Let G be a finite dimensional semisimple Lie algebra; we study the class of infinite dimensional representations of Gcalled characteristic p Verma modules. To obtain information about the structure of the Verma module Z(λ) we find primitive weights μ such that a non-zero homomorphism from Z(μ) to Z(λ) exists. For λ + ρ dominant, where ρ is the sum of the fundamental roots, there exist only finitely many primitive weights, and they all appear in a convex, bounded area. In the case of λ + ρ not dominant, and the characteristic p a good prime, there exist infinitely many primitive weights for the Lie algebra. For G = sl₃ we explicitly present a large, but not necessarily complete, set of primitive weights. A method to obtain the Verma module as the tensor product of Steinberg modules and Frobenius twisted Z(λ₁) is given for certain weights, λ = pⁿ λ₁ + (pⁿ — 1)ρ. Furthermore, a result about exact sequences of Weyl modules is carried over to Verma modules for sl₂. Finally, the connection between the subalgebra u¯₁ of the hyperalgebra U for a finite dimensional semisimple Lie algebra, and a group algebra KG for some suitable p-group G is studied. No isomorphism exists, when the characteristic of the field is larger than the Coxeter number. However, in the case of p — 2 we find u¯₁sl₃≈ KG. Furthermore, we determine the centre ofu¯_nsl₃, and we obtain an alternative K-basis of U-.

Thesis (Ph.D.)--Auburn University, 2005. / Abstract. Vita. Includes bibliographic references (ℓ. 43) and index.

Thesis (Ph.D.)--Baylor University, 2007. / In abstract "s and z " are subscript. Includes bibliographical references (p. 54-55).

Thesis (Master)--İzmir Institute of Technology, İzmir, 2005. / Keywords: Supplemented modules, cofinitely supplemented modules, cofinitely supplemented lattices, generalization of supplemented modules, generalization of cofinitely supplemented modules. Includes bibliographical references (leaves .p26).

Thesis (doctoral)--Universität Bonn, 1988. / Includes bibliographical references (p. 179-184).