Global ETD Search
Search theses and dissertations gathered from participating repositories worldwide. Every result links back to the library that holds it. No account is needed.
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Showing 1 to 20 of 47 for “"Injective"”.
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Injective objects
… with precisely one element. An R-module J is injective if and only if for every exact sequence 0→A→ [f above arrow] B of R-modules and R-homomorphisms and every R-homomorphism g: A→J there exists an R-homomorphism h: B→J such that hf = g. This is a dual concept to that of a projective …
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Gorenstein Injective Modules
… algebra is: when is the class of Gorenstein injective modules closed under arbitrary direct sums? Our main result gives a sufficient condition for this to happen. We prove that when the ring R is noetherian and such that every R-module has finite Gorenstein injective dimension, every direct …
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Projective and injective Banach spaces.
Thesis: Ph. D., Massachusetts Institute of Technology, Department of Mathematics, 1966
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A Systematic Study of Injective Envelopes
… in particular regarding injectivity and injective envelopes. We also compare the purely categorical definition of injectivity with the `standard' operator theoretical definition.
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The Baer Criterion For Injective Modules Over Noetherian Rings
… a test for checking to see if R-modules are injective modules. Then we considered the case when R is a Noetherian ring. We discovered that in this case we can refine our criteria for testing modules for injectivity.
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The Injective Envelope as the Space of Extremal Functions
In this thesis, we study the injective envelope of metric spaces by viewing it as the space of extremal functions as defined by Isbell. Extremal functions are also Kate˘tov functions, which satisfy two inequalities derived from the triangle inequality. One of these inequalities, along with a …
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On the theory of Krull rings and injective modules
… to our treatment of KRULL theory. The first is injective modules and.the second torsion theories. We then look at injective modules over Noetherian rings as in MATLIS [1958] and then over KRULL rings as in BECK [1971]. We show that for a KRULL ring there is a torsion theory (N,M) where N is the …
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Zero Divisors, Group Von Neumann Algebras and Injective Modules
In this thesis we discuss linear dependence of translations which is intimately related to the zero divisor conjecture. We also discuss the square integrable representations of the generalized Wyle-Heisenberg group in 𝑛² dimensions and its relations with Gabor's question from Gabor Analysis in the …
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Unitarily invariant norms and tensor products of maximal injective von Neumann subalgebras
… open question on the tensor product of maximal injective von Neumann subalgebras.</p><p>The first part of the dissertation is joint work with Don Hadwin, Eric Nordgren and Junhao Shen. The second part of the dissertation is joint work with Don Hadwin. This dissertation is partially supported by …
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Some generalizations of injectivity
… the direct sum of an extending module and an injective module is extending and when the direct sum of an extending module with the finite exchange property and a semisimple module is extending. We also characterize when the direct sum of a uniform-extending module and a semisimple module is …
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Diagonals of Tensor Products of Banach Lattices with Bases.
… projective tensor product and the positive injective tensor product of l_p space. Then by using these two main diagonals, we characterize the reflexivity, the property of being Kantorovich - Banach spaces, and the property of being order continuous of n-fold positive projective and positive …
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Extending modules relative to module classes
… modules over Dedekind domains. The importance of injective modules in Module Theory and more generally in Algebra is obvious in the 1960s and 1970s, largely, but not exclusively, through the impact of the publication of the lecture notes of Carl Faith [9]. Since that time there has been continuing …
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Foliations and exotic index theory
… that the analytic assembly map is rationally injective by using the exotic index theorem. The foliation exotic index theorem of S. Hurder is an extension of the theorem of G. Yu to the index theory for the foliations. Using the functorial property of the Kasparov KK-product, the foliation …
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Convexity in quasi-metric spaces
… thesis is to investigate the existence of an injective hull in the categories of T-quasi-metric spaces and of T-ultra-quasi-metric spaces with nonexpansive maps.
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Complexity over Finite-Dimensional Algebras
… we examine the Ω-complexity of a family of self-injective k-algebras where k is an algebraically closed field and Ω is the syzygy operator. More precisely, let T be the trivial extension of an iterated tilted algebra of type H. We prove that modules over the trivial extension T all have …
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Algebraically closed fields with characters; differential-henselian monotone valued differential fields
… the field of complex numbers and χ ∶ F → C is an injective, multiplication preserving map. In the second project we study the model theory of the differential-henselian monotone valued differential fields. We also consider definability in differential-henselian monotone fields with c-map and …
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Hyperconvex hulls in catergories of quasi-metric spaces
Isbell showed that every metric space has an injective hull, that is, every metric space has a “minimal” hyperconvex metric superspace. Dress then showed that the hyperconvex hull is a tight extension. In analogy to Isbell’s theory Kemajou et al. proved that each T₀-quasi-metric space X has a …
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Geometric Computing beyond the Laplacian
… to represent an arbitrary diffeomorphism or injective map that is possibly non-conformal, we search for a generalized Laplacian or elliptic PDE that accounts for quasi-conformal deformation and satisfies a prescribed Cauchy boundary condition; for geometric data interpolation, we search for …
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Goodwillie calculus and I
… using the indexing category of finite sets and injective maps in Goodwillie's calculus of homotopy functors. By careful analysis of the cross-effects of a reduced endofunctor of based spaces, this point of view leads to a monoidal model for the derivatives. Such structure induces operad and …
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Coefficient recovery in parabolic initial boundary value problems
… coefficient dependent observation operator is injective. With this knowledge, we use the Backus-Gilbert approach, modified with an adjoint method, to construct an approximate solution to the problem. We show the results of numerical experiments for the single, spatial variable case and then …
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