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Elsevier

North Holland

  • Transmutation, Scattering Theory and Special Functions

    • 1st Edition
    • Volume 69
    • R. Carroll
    • English

  • The Inverse Scattering Transformation and The Theory of Solitons

    • 1st Edition
    • Volume 50
    • W. Eckhaus + 1 more
    • English

  • Graded Ring Theory

    • 1st Edition
    • C. Nastasescu + 1 more
    • English
    This book is aimed to be a ‘technical’ book on graded rings. By ‘technical’ we mean that the book should supply a kit of tools of quite general applicability, enabling the reader to build up his own further study of non-commutative rings graded by an arbitrary group. The body of the book, Chapter A, contains: categorical properties of graded modules, localization of graded rings and modules, Jacobson radicals of graded rings, the structure thedry for simple objects in the graded sense, chain conditions, Krull dimension of graded modules, homogenization, homological dimension, primary decomposition, and more. One of the advantages of the generality of Chapter A is that it allows direct applications of these results to the theory of group rings, twisted and skew group rings and crossed products. With this in mind we have taken care to point out on several occasions how certain techniques may be specified to the case of strongly graded rings. We tried to write Chapter A in such a way that it becomes suitable for an advanced course in ring theory or general algebra, we strove to make it as selfcontained as possible and we included several problems and exercises. Other chapters may be viewed as an attempt to show how the general techniques of Chapter A can be applied in some particular cases, e.g. the case where the gradation is of type Z. In compiling the material for Chapters B and C we have been guided by our own research interests. Chapter 6 deals with commutative graded rings of type 2 and we focus on two main topics: artihmeticallygraded domains, and secondly, local conditions for Noetherian rings. In Chapter C we derive some structural results relating to the graded properties of the rings considered. The following classes of graded rings receive special attention: fully bounded Noetherian rings, birational extensions of commutative rings, rings satisfying polynomial identities, and Von Neumann regular rings. Here the basic idea is to derive results of ungraded nature from graded information. Some of these sections lead naturally to the study of sheaves over the projective spectrum Proj(R) of a positively graded ring, but we did not go into these topics here. We refer to [125] for a noncommutative treatment of projective geometry, i.e. the geometry of graded P.I. algebras.

  • Differential Calculus and Holomorphy

    Real and Complex Analysis in Locally Convex Spaces
    • 1st Edition
    • Volume 64
    • J.F. Colombeau
    • English

  • Methods of Differential Geometry in Analytical Mechanics

    • 1st Edition
    • Volume 158
    • M. de León + 1 more
    • English
    The differential geometric formulation of analytical mechanics not only offers a new insight into Mechanics, but also provides a more rigorous formulation of its physical content from a mathematical viewpoint.Topics covered in this volume include differential forms, the differential geometry of tangent and cotangent bundles, almost tangent geometry, symplectic and pre-symplectic Lagrangian and Hamiltonian formalisms, tensors and connections on manifolds, and geometrical aspects of variational and constraint theories.The book may be considered as a self-contained text and only presupposes that readers are acquainted with linear and multilinear algebra as well as advanced calculus.

  • Second Order Linear Differential Equations in Banach Spaces

    • 1st Edition
    • Volume 108
    • H.O. Fattorini
    • English
    Second order linear differential equations in Banach spaces can be used for modelling such second order equations of mathematical physics as the wave equation, the Klein-Gordon equation, et al. In this way, a unified treatment can be given to subjects such as growth of solutions, singular perturbation of parabolic, hyperbolic and Schrödinger type initial value problems, and the like. The book covers in detail these subjects as well as the applications to each specific problem.

  • Spectral Transform and Solitons

    • 1st Edition
    • Volume 13
    • F. Calogero + 1 more
    • English

  • Holomorphic Automorphism Groups in Banach Spaces

    An Elementary Introduction
    • 1st Edition
    • Volume 105
    • J.M. Isidro + 1 more
    • English

  • Mathematical Models in Environmental Problems

    • 1st Edition
    • Volume 16
    • G.I. Marchuk
    • English

  • Mathematicians and Their Times

    • 1st Edition
    • Volume 48
    • L. Young
    • English

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