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On Herstein's conjecture and primary decompositionCovington, Ashley January 2001 (has links)
No description available.
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Injective modules and representational repletenessLow, Gordan MacLaren January 1993 (has links)
No description available.
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Ranks and bounds for indecomposable modules over one-dimensional Noetherian ringsLuckas, Melissa R. January 1900 (has links)
Thesis (Ph.D.)--University of Nebraska-Lincoln, 2007. / Title from title screen (site viewed Apr. 29, 2008). PDF text: 103 p. : ill. ; 493 K. UMI publication number: AAT 3283908. Includes bibliographical references. Also available in microfilm and microfiche formats.
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Some Properties of Noetherian RingsVaughan, Stephen N. (Stephen Nick) 05 1900 (has links)
This paper is an investigation of several basic properties of noetherian rings. Chapter I gives a brief introduction, statements of definitions, and statements of theorems without proof. Some of the main results in the study of noetherian rings are proved in Chapter II. These results include proofs of the equivalence of the maximal condition, the ascending chain condition, and that every ideal is finitely generated. Some other results are that if a ring R is noetherian, then R[x] is noetherian, and that if every prime ideal of a ring R is finitely generated, then R is noetherian.
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Non-prime Dedeking ordersLissaman, Richard January 1997 (has links)
No description available.
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H-LOCAL RINGSUnknown Date (has links)
We say that a commutative ring R has the unique decomposition into ideals (UDI) property if, for any R-module which decomposes into a _nite direct sum of indecomposable ideals, this decomposition is unique up to the order and isomorphism class of the ideals. In a 2001 paper, Goeters and Olberding characterize the UDI property for Noetherian integral domains and in a 2011 paper Ay and Klingler obtain similar results for Noetherian reduced rings. We characterize the UDI property for Noetherian rings in general. / Includes bibliography. / Dissertation (Ph.D.)--Florida Atlantic University, 2019. / FAU Electronic Theses and Dissertations Collection
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Ore localization and the Ischebeck spectral sequenceVyas, Rishi January 2013 (has links)
No description available.
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Associated primes over Ore extensions and generalized Weyl algebras /Nordstrom, Hans Erik, January 2005 (has links)
Thesis (Ph. D.)--University of Oregon, 2005. / Typescript. Includes vita and abstract. Includes bibliographical references (leaves 48-49). Also available for download via the World Wide Web; free to University of Oregon users.
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On lie and Noether symmetries of differential equations.Kara, A. H. January 1994 (has links)
A thesis submitted to the faculty of Science, University of the Witwatersrand, in
fulfilment of the requirements for the degree of Doctor of Philosophy, / The inverse problem in the Calculus of Variations involves determining the Lagrangians,
if any, associated with a given (system of) differential equation(s). One
can classify Lagrangians according to the Lie algebra of symmetries of the Action
integral (the Noether algebra). We give a complete classification of first-order Lagrangians
defined on the line and produce results pertaining to the dimensionality
of the algebra of Noether symmetries and compare and contrast these with similar
results on the algebra of Lie symmetries of the corresponding Euler-Lagrange .equations.
It is proved that the maximum dimension of the Noether point symmetry
algebra of a particle Lagrangian. is five whereas it is known that the maximum dimension
Qf the Lie algebra of the corresponding scalar second-order Euler-Lagrange
equation is eight. Moreover, we show th'a.t a particle Lagrangian does not admit a
maximal four-dimensional Noether point symmeiry algebra and consequently a particle
Lagrangian admits the maximal r E {O, 1,2,3, 5}-dimensional Noether point
symmetry algebra,
It is well .known that an important means of analyzing differential equations lies in
the knowledge of the first integrals of the equation. We deliver an algorithm for
finding first integrals of partial differential equations and show how some of the
symmetry properties of the first integrals help to 'further' reduce the order of the
equations and sometimes completely solve the equations.
Finally, we discuss some open questions. These include the inverse problem and
classification of partial differential equations. ALo, there is the question of the
extension of the results to 'higher' dimensions. / Andrew Chakane 2018
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Symmetries and conservation laws of higher-order PDEsNarain, R. B. 19 January 2012 (has links)
PhD., Faculty of Science, University of the Witwatersrand, 2011 / The construction of conserved vectors using Noether’s theorem via a knowledge
of a Lagrangian (or via the recently developed concept of partial Lagrangians) is
well known. The formulae to determine these for higher-order flows is somewhat
cumbersome and becomes more so as the order increases. We carry out these for
a class of fourth, fifth and sixth order PDEs. In the latter case, we involve the
fifth-order KdV equation using the concept of ‘weak’ Lagrangians better known for
the third-order KdV case.
We then consider the case of a mixed ‘high-order’ equations working on the Shallow
Water Wave and Regularized Long Wave equations. These mixed type equations
have not been dealt with thus far using this technique. The construction of conserved
vectors using Noether’s theorem via a knowledge of a Lagrangian is well known.
In some of the examples, our focus is that the resultant conserved flows display some
previously unknown interesting ‘divergence properties’ owing to the presence of the
mixed derivatives.
We then analyse the conserved flows of some multi-variable equations that arise
in Relativity. In addition to a larger class of conservation laws than those given
by the isometries or Killing vectors, we may conclude what the isometries are and
that these form a Lie subalgebra of the Noether symmetry algebra. We perform
our analysis on versions of the Vaidya metric yielding some previously unknown
information regarding the corresponding manifold. Lastly, with particular reference
to this metric, we also show the variations that occur for the unknown functions.
We discuss symmetries of classes of wave equations that arise as a consequence
of the Vaidya metric. The objective of this study is to show how the respective
geometry is responsible for giving rise to a nonlinear inhomogeneous wave equation
as an alternative to assuming the existence of nonlinearities in the wave equation
due to physical considerations. We find Lie and Noether point symmetries of the
corresponding wave equations and give some reductions. Some interesting physical
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conclusions relating to conservation laws such as energy, linear and angular momenta
are also determined. We also present some interesting comparisons with the standard
wave equations (on a ‘flat geometry’).
Finally, we pursue the nature of the flow of a third grade fluid with regard to
its underlying conservation laws. In particular, the fluid occupying the space over
a wall is considered. At the surface of the wall, suction or blowing velocity is
applied. By introducing a velocity field, the governing equations are reduced to a
class of PDEs. A complete class of conservation laws for the resulting equations
are constructed and analysed using the invariance properties of the corresponding
multipliers/characteristics.
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