Faithfully Quadratic Rings
DOWNLOAD
FREE 30 Days
Download Faithfully Quadratic Rings PDF/ePub or read online books in Mobi eBooks. Click Download or Read Online button to get Faithfully Quadratic Rings book now. This website allows unlimited access to, at the time of writing, more than 1.5 million titles, including hundreds of thousands of titles in various foreign languages. If the content not found or just blank you must refresh this page
Faithfully Quadratic Rings
DOWNLOAD
FREE 30 Days
Author : M. A. Dickmann
language : en
Publisher:
Release Date : 2015
Faithfully Quadratic Rings written by M. A. Dickmann and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015 with Commutative rings categories.
In this monograph we extend the classical algebraic theory of quadratic forms over fields to diagonal quadratic forms with invertible entries over broad classes of commutative, unitary rings where -1 is not a sum of squares and 2 is invertible. We accomplish this by: (1) Extending the classical notion of matrix isometry of forms to a suitable notion of T-isometry, where T is a preorder of the given ring, A, or T = A2. (2) Introducing in this context three axioms expressing simple properties of (value) representation of elements of the ring by quadratic forms, well-known to hold in the field case. Under these axioms we prove that the ring-theoretic approach based on T-isometry coincides with the formal approach formulated in terms of reduced special groups. This guarantees, for rings verifying these axioms, the validity of a number of important structural properties, notably the Arason-Pfister Hauptsatz, Milnor's mod 2 Witt ring conjecture, Marshall's signature conjecture, uniform upper bounds for the Pfister index of quadratic forms, a local-global Sylvester inertia law, etc. We call (T)-faithfully quadratic rings verifying these axioms. A significant part of the monograph is devoted to prove quadratic faithfulness of certain outstanding (classes of) rings; among them, rings with many units satisfying a mild additional requirement, reduced f-rings (herein rings of continuous real-valued functions), and strictly representable rings. Obviously, T-quadratic faithfulness depends on both the ring and the preorder T. We isolate a property of preorders defined solely in terms of the real spectrum of a given ring -- that we baptise unit-reflecting preorders -- which, for an extensive class of preordered rings, (A, T), turns out to be equivalent to the T-quadratic faithfulness of A. We show, e.g., that all preorders on the ring of continuous real-valued functions on a compact Hausdorff are unit-reflecting; we also give examples where this property fails.
Faithfully Quadratic Rings
DOWNLOAD
FREE 30 Days
Author : M. Dickmann
language : en
Publisher: American Mathematical Soc.
Release Date : 2015-10-27
Faithfully Quadratic Rings written by M. Dickmann and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-10-27 with Commutative rings categories.
In this monograph the authors extend the classical algebraic theory of quadratic forms over fields to diagonal quadratic forms with invertible entries over broad classes of commutative, unitary rings where is not a sum of squares and is invertible. They accomplish this by: (1) Extending the classical notion of matrix isometry of forms to a suitable notion of -isometry, where is a preorder of the given ring, , or . (2) Introducing in this context three axioms expressing simple properties of (value) representation of elements of the ring by quadratic forms, well-known to hold in the field case.
Quadratic Forms Over Semilocal Rings
DOWNLOAD
FREE 30 Days
Author : R. Baeza
language : en
Publisher: Springer
Release Date : 2006-11-22
Quadratic Forms Over Semilocal Rings written by R. Baeza and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-22 with Mathematics categories.
Diagonalizing Quadratic Bosonic Operators By Non Autonomous Flow Equations
DOWNLOAD
FREE 30 Days
Author : Volker Bach
language : en
Publisher: American Mathematical Soc.
Release Date : 2016-03-10
Diagonalizing Quadratic Bosonic Operators By Non Autonomous Flow Equations written by Volker Bach and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-03-10 with Hamiltonian operator categories.
The authors study a non-autonomous, non-linear evolution equation on the space of operators on a complex Hilbert space. They specify assumptions that ensure the global existence of its solutions and allow them to derive its asymptotics at temporal infinity. They demonstrate that these assumptions are optimal in a suitable sense and more general than those used before. The evolution equation derives from the Brocket-Wegner flow that was proposed to diagonalize matrices and operators by a strongly continuous unitary flow. In fact, the solution of the non-linear flow equation leads to a diagonalization of Hamiltonian operators in boson quantum field theory which are quadratic in the field.
Ordered Algebraic Structures And Related Topics
DOWNLOAD
FREE 30 Days
Author : Fabrizio Broglia
language : en
Publisher: American Mathematical Soc.
Release Date : 2017
Ordered Algebraic Structures And Related Topics written by Fabrizio Broglia and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017 with Forms, Quadratic categories.
This volume contains the proceedings of the international conference ""Ordered Algebraic Structures and Related Topics'', held from October 12-16, 2015, at CIRM, Luminy, Marseilles, France. Papers contained in this volume cover topics in real analytic geometry, real algebra, and real algebraic geometry including complexity issues, model theory of various algebraic and differential structures, Witt equivalence of fields, and the moment problem.
Quadratic And Hermitian Forms Over Rings
DOWNLOAD
FREE 30 Days
Author : Max-Albert Knus
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Quadratic And Hermitian Forms Over Rings written by Max-Albert Knus and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
From its birth (in Babylon?) till 1936 the theory of quadratic forms dealt almost exclusively with forms over the real field, the complex field or the ring of integers. Only as late as 1937 were the foundations of a theory over an arbitrary field laid. This was in a famous paper by Ernst Witt. Still too early, apparently, because it took another 25 years for the ideas of Witt to be pursued, notably by Albrecht Pfister, and expanded into a full branch of algebra. Around 1960 the development of algebraic topology and algebraic K-theory led to the study of quadratic forms over commutative rings and hermitian forms over rings with involutions. Not surprisingly, in this more general setting, algebraic K-theory plays the role that linear algebra plays in the case of fields. This book exposes the theory of quadratic and hermitian forms over rings in a very general setting. It avoids, as far as possible, any restriction on the characteristic and takes full advantage of the functorial aspects of the theory. The advantage of doing so is not only aesthetical: on the one hand, some classical proofs gain in simplicity and transparency, the most notable examples being the results on low-dimensional spinor groups; on the other hand new results are obtained, which went unnoticed even for fields, as in the case of involutions on 16-dimensional central simple algebras. The first chapter gives an introduction to the basic definitions and properties of hermitian forms which are used throughout the book.
Relative Nonhomogeneous Koszul Duality
DOWNLOAD
FREE 30 Days
Author : Leonid Positselski
language : en
Publisher: Springer Nature
Release Date : 2022-02-10
Relative Nonhomogeneous Koszul Duality written by Leonid Positselski and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-02-10 with Mathematics categories.
This research monograph develops the theory of relative nonhomogeneous Koszul duality. Koszul duality is a fundamental phenomenon in homological algebra and related areas of mathematics, such as algebraic topology, algebraic geometry, and representation theory. Koszul duality is a popular subject of contemporary research. This book, written by one of the world's leading experts in the area, includes the homogeneous and nonhomogeneous quadratic duality theory over a nonsemisimple, noncommutative base ring, the Poincare–Birkhoff–Witt theorem generalized to this context, and triangulated equivalences between suitable exotic derived categories of modules, curved DG comodules, and curved DG contramodules. The thematic example, meaning the classical duality between the ring of differential operators and the de Rham DG algebra of differential forms, involves some of the most important objects of study in the contemporary algebraic and differential geometry. For the first time in the history of Koszul duality the derived D-\Omega duality is included into a general framework. Examples highly relevant for algebraic and differential geometry are discussed in detail.
Proof Of The 1 Factorization And Hamilton Decomposition Conjectures
DOWNLOAD
FREE 30 Days
Author : Béla Csaba
language : en
Publisher: American Mathematical Soc.
Release Date : 2016-10-05
Proof Of The 1 Factorization And Hamilton Decomposition Conjectures written by Béla Csaba and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-10-05 with 1-factorization categories.
In this paper the authors prove the following results (via a unified approach) for all sufficiently large n: (i) [1-factorization conjecture] Suppose that n is even and D≥2⌈n/4⌉−1. Then every D-regular graph G on n vertices has a decomposition into perfect matchings. Equivalently, χ′(G)=D. (ii) [Hamilton decomposition conjecture] Suppose that D≥⌊n/2⌋. Then every D-regular graph G on n vertices has a decomposition into Hamilton cycles and at most one perfect matching. (iii) [Optimal packings of Hamilton cycles] Suppose that G is a graph on n vertices with minimum degree δ≥n/2. Then G contains at least regeven(n,δ)/2≥(n−2)/8 edge-disjoint Hamilton cycles. Here regeven(n,δ) denotes the degree of the largest even-regular spanning subgraph one can guarantee in a graph on n vertices with minimum degree δ. (i) was first explicitly stated by Chetwynd and Hilton. (ii) and the special case δ=⌈n/2⌉ of (iii) answer questions of Nash-Williams from 1970. All of the above bounds are best possible.
The Abc Problem For Gabor Systems
DOWNLOAD
FREE 30 Days
Author : Xin-Rong Dai
language : en
Publisher: American Mathematical Soc.
Release Date : 2016-10-05
The Abc Problem For Gabor Systems written by Xin-Rong Dai and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-10-05 with Gabor frames categories.
A longstanding problem in Gabor theory is to identify time-frequency shifting lattices aZ×bZ and ideal window functions χI on intervals I of length c such that {e−2πinbtχI(t−ma): (m,n)∈Z×Z} are Gabor frames for the space of all square-integrable functions on the real line. In this paper, the authors create a time-domain approach for Gabor frames, introduce novel techniques involving invariant sets of non-contractive and non-measure-preserving transformations on the line, and provide a complete answer to the above abc-problem for Gabor systems.
Monoidal Categories And The Gerstenhaber Bracket In Hochschild Cohomology
DOWNLOAD
FREE 30 Days
Author : Reiner Hermann:
language : en
Publisher: American Mathematical Soc.
Release Date : 2016-09-06
Monoidal Categories And The Gerstenhaber Bracket In Hochschild Cohomology written by Reiner Hermann: and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-09-06 with Associative rings categories.
In this monograph, the author extends S. Schwede's exact sequence interpretation of the Gerstenhaber bracket in Hochschild cohomology to certain exact and monoidal categories. Therefore the author establishes an explicit description of an isomorphism by A. Neeman and V. Retakh, which links Ext-groups with fundamental groups of categories of extensions and relies on expressing the fundamental group of a (small) category by means of the associated Quillen groupoid. As a main result, the author shows that his construction behaves well with respect to structure preserving functors between exact monoidal categories. The author uses his main result to conclude, that the graded Lie bracket in Hochschild cohomology is an invariant under Morita equivalence. For quasi-triangular bialgebras, he further determines a significant part of the Lie bracket's kernel, and thereby proves a conjecture by L. Menichi. Along the way, the author introduces n-extension closed and entirely extension closed subcategories of abelian categories, and studies some of their properties.