Examples of this include the study of ideals and divisibility, dating back to the work of Dedekind and continued by Krull; the pioneering work of Hahn on totally ordered abelian groups; and the work of Kantorovich and other analysts on ...
Author: M.E Anderson
Publisher: Springer Science & Business Media
The study of groups equipped with a compatible lattice order ("lattice-ordered groups" or "I!-groups") has arisen in a number of different contexts. Examples of this include the study of ideals and divisibility, dating back to the work of Dedekind and continued by Krull; the pioneering work of Hahn on totally ordered abelian groups; and the work of Kantorovich and other analysts on partially ordered function spaces. After the Second World War, the theory of lattice-ordered groups became a subject of study in its own right, following the publication of fundamental papers by Birkhoff, Nakano and Lorenzen. The theory blossomed under the leadership of Paul Conrad, whose important papers in the 1960s provided the tools for describing the structure for many classes of I!-groups in terms of their convex I!-subgroups. A particularly significant success of this approach was the generalization of Hahn's embedding theorem to the case of abelian lattice-ordered groups, work done with his students John Harvey and Charles Holland. The results of this period are summarized in Conrad's "blue notes" [C].
Proceedings of the Curaçao Conference, sponsored by the Caribbean
Mathematics Foundation, June 26–30, 1995 W.C. Holland, Jorge Martínez. 3. ... Lattice-Ordered Groups, an Introduction. Reidel Texts in the Mathematical Sciences. Reidel ...
Author: W.C. Holland
Publisher: Springer Science & Business Media
The conference on Ordered Algebraic Structures held in Curat;ao, from the 26th of June through the 30th of June, 1995, at the Avila Beach Hotel, marked the eighth year of ac tivities by the Caribbean Mathematics Foundation (abbr. CMF), which was the principal sponsor of this conference. CMF was inaugurated in 1988 with a conference on Ordered Algebraic Structures. During the years between these two conferences the field has changed sufficiently, both from my point of view and, I believe, that of my co-organizer, W. Charles Holland, to make one wonder about the label "Ordered Algebraic Structures" itself. We recognized this from the start, and right away this conference carried a subtitle, or, if one prefers, an agenda: we concentrated on the one hand, on traditional themes in the theory of ordered groups, including model-theoretic aspects, and, on the other hand, on matters in which topology (more precisely C(X)-style topology) and category theory would play a prominent role. Plainly, ordered algebra has many faces, and it is becoming increas ingly difficult to organize an intimate conference, such as the ones encouraged in the series sponsored by CMF, in this area on a broad set of themes. These proceedings reflect, accurately we think, the spirit of the conferees, but it is not a faithful record of the papers presented at the conference.
In: S. Abramsky, G.M. Gabbay, and T.S.E. Maibaum, editors, Handbook of logic in
computer science, vol. 3, 1–168, Handb. Log. ...  M. Anderson and T. Feil, Lattice-Ordered Groups. An Introduction. Reidel Texts in the Mathematical Sciences ...
Author: George Grätzer
George Grätzer's Lattice Theory: Foundation is his third book on lattice theory (General Lattice Theory, 1978, second edition, 1998). In 2009, Grätzer considered updating the second edition to reflect some exciting and deep developments. He soon realized that to lay the foundation, to survey the contemporary field, to pose research problems, would require more than one volume and more than one person. So Lattice Theory: Foundation provided the foundation. Now we complete this project with Lattice Theory: Special Topics and Applications, written by a distinguished group of experts, to cover some of the vast areas not in Foundation. This first volume is divided into three parts. Part I. Topology and Lattices includes two chapters by Klaus Keimel, Jimmie Lawson and Ales Pultr, Jiri Sichler. Part II. Special Classes of Finite Lattices comprises four chapters by Gabor Czedli, George Grätzer and Joseph P. S. Kung. Part III. Congruence Lattices of Infinite Lattices and Beyond includes four chapters by Friedrich Wehrung and George Grätzer.
... biology , and mathematical economics Marius Tucsnak Marlow Anderson and
Todd Feil , Lattice - Ordered Groups . An Introduction . Reiilo Texts in the Mathematical Sciences . D . Reidel Publishing Company , Kluwer Academic
An appendix discusses applications to the classification problem of computer science , as developed by Budach in ... From the introduction : “ In this paper , we
study a family of lattices which we call generalized Dowling lattices . ... on the
finite group G . In this paper we study combinatorial properties of the generalized
Dowling lattices and their order complexes . ... From the text : “ The extension
problem for groups is as follows : Given two groups H , K , construct all groups G
1985. text ed. 79.00 (ISBN 90-6191-596-1, Pub by A A Balkema). Brookfield Pub
Co. Keegan, William F., ed. Emergent Horticultural Economies of the ... Tropical
Timber for Building Materials in the Andean Group Countries of South America.
D Reidel Pub, 1982, xviii + 966 pp., $99. ... Twenty-three survey articles touching
upon all areas of current research on ordered sets, from set theory and recursion,
to lattice theory and enumeration problems, to applications in computer and
social sciences. ... JS Number theory, r(18), P. Introduction to cyclotomic Fields.
Lawrence C. Washington. Grad. Texts in Math., v. ... The first part contains six
chapters: Sources of Algebra; Vector Spaces; Determinants; Algebraic Structures
SIAM J. Math. Anal. 11 (1980), no. 2, 316–339. (Aubrey B. Poore) 82i:80010
58C28.0090 80A30 (58C28) Introduction ... 58E07 (35B32, 47H15, 58C27,
76E15, 76R99) The Bénard problem, symmetry and the lattice of isotropy
subgroups. ... (From the text) 85h:58127 58F14.0777 58F14 (with Swift, James W.
; Knobloch, Edgar) Symmetries and pattern ... (Jurgen Scheurle) 86c:58027
58E07.0481 58E07 (76E15) (with Schaeffer, David G.) & Singularities and groups in bifurcation theory.
(From the text) 85f:46016 46A40 Kolesnik, T. V. (with Dzhuraev, I. N.) Application
of exact difference schemes to the estimation of the rate of convergence of the
method of nets for second-order hyperbolic equations. (Russian) ... Abelian group theory (Honolulu, Hawaii, 1983), 696–710, Lecture Notes in Math., 1006,
Springer, Berlin-New York, 1983. ... (Author's introduction) 85k:06003 06A10 (
90A14) Compatible orderings in semilattices. ... in the physico-mathematical sciences.
Probability & Math Statistics S. E57.45 Wiley (381) 0 471 02723 5 Order Upon the
Land United States Rectangular land Survey and ... N.A.T.O.Advanced Study inst
S. f62.25 Reidel Pub. ... Medieval Texts, £3000 Oxf U.P. (575) 0 19822232 7 v.6.
Bks.11-13. Tr.fr Latin. Ed M.Chibnall. D8.640. Medieval Texts ... Lattices.Ordered Groups.Topology, Theory of Models and Relations.Combinatorics Effectiveness
Social Sciences – Conference Proceedings (Ed. Pouzet & Richard) M8xxx,552.
Lattice 1 . Analytic functions . 2 . Manifolds Cambridge University Press , 1975 . xi
, 121 Science Foundation and the ... I . Title . translated and adapted from the
Russian Prepared from C . I . P . groups - Congresses . ... B29 1976 ) 75 - 15979
ISBN 0 - 471 - 05464 - X : Fundamentals to complex analysis for mathematics , science , and ... N68 ] 74 - 7098 ISBN Introduction to spectral theory : selfadjoint
Includes bibliographical references and An introduction to complex analysis / P .
0 - 06 ...
Twistors have , in recent years , attracted increasing attention as a mathematical
tool and as a means of gaining new ... Besides high scientific interest in the
sometimes unique or unusual properties , e.g. , at low temperatures , a lot of data
... Consequently the different fields of research were introduced by so - called
basic lectures followed ... Prokhovnik , S.J. ( School of Mathematics , New South
Wales Univ . ( Australia ) . ISBN 90-277-2093-2 Dordrecht ( Netherlands ) . Reidel . 1985.
Radial parts of the Laplace operators on the Lie supergroups Ulp , 9 ) and C ( m ,
n ) . ... an eminent Russian mathematician , died in 1980 , and the present
volume has been updated , arranged and explicated by the ... The first chapter is
an overview of the various branches of supermathematics . ... Note : Basic introductory text suited to ... Includes new sections which cover electron waves ,
amorphous semiconductors , quantum wells and superlattices . ... For college science libraries .