On Totally Ordered Groups And K0
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On Totally Ordered Groups And K0
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Author : George A. Elliott
language : en
Publisher:
Release Date : 1978
On Totally Ordered Groups And K0 written by George A. Elliott and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1978 with categories.
Partially Ordered Abelian Groups With Interpolation
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Author : K. R. Goodearl
language : en
Publisher: American Mathematical Soc.
Release Date : 2010-05-30
Partially Ordered Abelian Groups With Interpolation written by K. R. Goodearl 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 2010-05-30 with Mathematics categories.
A branch of ordered algebraic structures has grown, motivated by $K$-theoretic applications and mainly concerned with partially ordered abelian groups satisfying the Riesz interpolation property. This monograph is the first source in which the algebraic and analytic aspects of these interpolation groups have been integrated into a coherent framework for general reference. The author provides a solid foundation in the structure theory of interpolation groups and dimension groups (directed unperforated interpolation groups), with applications to ordered $K$-theory particularly in mind. Although interpolation groups are defined as purely algebraic structures, their development has been strongly influenced by functional analysis. This cross-cultural development has left interpolation groups somewhat estranged from both the algebraists, who may feel intimidated by compact convex sets, and the functional analysts, who may feel handicapped by the lack of scalars. This book, requiring only standard first-year graduate courses in algebra and functional analysis, aims to make the subject accessible to readers from both disciplines.High points of the development include the following: characterization of dimension groups as direct limits of finite products of copies of the integers; the double-dual representation of an interpolation group with order-unit via affine continuous real-valued functions on its state space; the structure of dimension groups complete with respect to the order-unit norm, as well as monotone sigma-complete dimension groups and dimension groups with countably infinite interpolation; and an introduction to the problem of classifying extensions of one dimension group by another. The book also includes a development of portions of the theory of compact convex sets and Choquet simplices, and an expository discussion of various applications of interpolation group theory to rings and $C DEGREES*$-algebras via ordered $K_0$. A discussion of some open problems in interpolation groups and dimension groups concludes the book.Of interest, of course, to researchers in ordered algebraic structures, the book will also be a valuable source for researchers seeking a background in interpolation groups and dimension groups for applications to such subjects as rings, operator algebras, topological Markov chains, positive polynomials, compact group actions, or other areas where ordered Grothendieck groups might be useful. This is a reprint of the 1986 original. (SUR
Ordered Groups And Infinite Permutation Groups
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Author : W.C. Holland
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-12-01
Ordered Groups And Infinite Permutation Groups written by W.C. Holland 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 2013-12-01 with Mathematics categories.
The subjects of ordered groups and of infinite permutation groups have long en joyed a symbiotic relationship. Although the two subjects come from very different sources, they have in certain ways come together, and each has derived considerable benefit from the other. My own personal contact with this interaction began in 1961. I had done Ph. D. work on sequence convergence in totally ordered groups under the direction of Paul Conrad. In the process, I had encountered "pseudo-convergent" sequences in an ordered group G, which are like Cauchy sequences, except that the differences be tween terms of large index approach not 0 but a convex subgroup G of G. If G is normal, then such sequences are conveniently described as Cauchy sequences in the quotient ordered group GIG. If G is not normal, of course GIG has no group structure, though it is still a totally ordered set. The best that can be said is that the elements of G permute GIG in an order-preserving fashion. In independent investigations around that time, both P. Conrad and P. Cohn had showed that a group admits a total right ordering if and only if the group is a group of automor phisms of a totally ordered set. (In a right ordered group, the order is required to be preserved by all right translations, unlike a (two-sided) ordered group, where both right and left translations must preserve the order.
On Totally Ordered Groups
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Author :
language : en
Publisher:
Release Date : 1978
On Totally Ordered Groups written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1978 with categories.
Fully Ordered Groups
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Author : Aleksandr Ilʹich Kokorin
language : en
Publisher:
Release Date : 1974
Fully Ordered Groups written by Aleksandr Ilʹich Kokorin and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1974 with Linear algebraic groups categories.
Partially Ordered Groups
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Author : A M W Glass
language : en
Publisher: World Scientific
Release Date : 1999-07-22
Partially Ordered Groups written by A M W Glass and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999-07-22 with Mathematics categories.
Recently the theory of partially ordered groups has been used by analysts, algebraists, topologists and model theorists. This book presents the most important results and topics in the theory with proofs that rely on (and interplay with) other areas of mathematics. It concludes with a list of some unsolved problems for the reader to tackle. In stressing both the special techniques of the discipline and the overlap with other areas of pure mathematics, the book should be of interest to a wide audience in diverse areas of mathematics.
Ordered Algebraic Structures
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Author : W. B. Powell
language : en
Publisher: CRC Press
Release Date : 1985-10-01
Ordered Algebraic Structures written by W. B. Powell and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1985-10-01 with Mathematics categories.
The papers contained in this volume constitute the proceedings of the Special Session on Ordered Algebraic Structures which was held at the 1982 annual meeting of the American Mathematical Society in Cincinnati, Ohio. The Special Session and this volume honor Paul Conrad, whose work on the subject is noted for its depth and originality. These papers address many areas within the subject of ordered algebraic structures, including varieties, free algebras, lattice ordered groups, subgroups of ordered groups, semigroups, ordered rings, and topological properties of these structures.
Lattice Ordered Groups
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Author : A.M. Glass
language : en
Publisher: Springer Science & Business Media
Release Date : 1989-03-31
Lattice Ordered Groups written by A.M. Glass 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 1989-03-31 with Mathematics categories.
A lattice-ordered group is a mathematical structure combining a (partial) order (lattice) structure and a group structure (on a set) in a compatible way. Thus it is a composite structure, or, a set carrying two or more simple structures in a compatible way. The field of lattice-ordered groups turn up on a wide range of mathematical fields ranging from functional analysis to universal algebra. These papers address various aspects of the field, with wide applicability for interested researchers.
Theory Of Lattice Ordered Groups
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Author : Michael Darnel
language : en
Publisher: CRC Press
Release Date : 1994-11-15
Theory Of Lattice Ordered Groups written by Michael Darnel and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1994-11-15 with Mathematics categories.
Provides a thorough discussion of the orderability of a group. The book details the major developments in the theory of lattice-ordered groups, delineating standard approaches to structural and permutation representations. A radically new presentation of the theory of varieties of lattice-ordered groups is offered.;This work is intended for pure and applied mathematicians and algebraists interested in topics such as group, order, number and lattice theory, universal algebra, and representation theory; and upper-level undergraduate and graduate students in these disciplines.;College or university bookstores may order five or more copies at a special student price which is available from Marcel Dekker Inc, upon request.
K Theory Of Finite Groups And Orders
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Author : Richard G. Swan
language : en
Publisher: Springer
Release Date : 2006-11-15
K Theory Of Finite Groups And Orders written by Richard G. Swan and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-15 with Mathematics categories.