Lattice-Ordered Groups, A.M. Glass; W.C. Holland

Автор: T.S. Blyth
Название: Lattices and Ordered Algebraic Structures
ISBN: 1849969558 ISBN-13(EAN): 9781849969550
Издательство: Springer
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Описание: "The text can serve as an introduction to fundamentals in the respective areas from a residuated-maps perspective and with an eye on coordinatization.

Автор: Steven Roman
Название: Lattices and Ordered Sets
ISBN: 1441927042 ISBN-13(EAN): 9781441927040
Издательство: Springer
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Описание: Lattice theory began in the early 1890s, when Richard Dedekind wanted to know the answer to the following question: Given three subgroups EF , and G of an abelian group K, what is the largest number of distinct subgroups that can be formed using these subgroups and the operations of intersection and sum (join), as in E?FssDE?FN?GssE?DF?GN and so on?

Автор: Gr?tzer
Название: Lattice Theory: Special Topics and Applications
ISBN: 331944235X ISBN-13(EAN): 9783319442358
Издательство: Springer
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Описание: George Gr?tzer's Lattice Theory: Foundation is his third book on lattice theory (General Lattice Theory, 1978, second edition, 1998). In 2009, Gr?tzer 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, in two volumes, written by a distinguished group of experts, to cover some of the vast areas not in Foundation. This second volume is divided into ten chapters contributed by K. Adaricheva, N. Caspard, R. Freese, P. Jipsen, J.B. Nation, N. Reading, H. Rose, L. Santocanale, and F. Wehrung.

Автор: Sen, Dr. Soumya Cortesi, Agostino Chaki, Nabendu
Название: Hyper-lattice algebraic model for data warehousing
ISBN: 3319280422 ISBN-13(EAN): 9783319280424
Издательство: Springer
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Описание: This book presents Hyper-lattice, a new algebraic model for partially ordered sets, and an alternative to lattice. The authors analyze some of the shortcomings of conventional lattice structure and propose a novel algebraic structure in the form of Hyper-lattice to overcome problems with lattice.

Автор: Jorge Mart?nez
Название: Ordered Algebraic Structures
ISBN: 0792304896 ISBN-13(EAN): 9780792304890
Издательство: Springer
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Описание: Proceedings of the Caribbean Mathematics Foundation Conference, held in Curacao, August 1988

Автор: Jorge Mart?nez; W.C. Holland
Название: Ordered Algebraic Structures
ISBN: 0792322584 ISBN-13(EAN): 9780792322580
Издательство: Springer
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Описание: A selection of papers from the 1991 Conrad Conference, held in Gainesville, Florida. They give an overview of some recent advances in the area of ordered algebraic structures. Topics covered include ordered permutation groups and universal, as well as model-theoretic, aspects.

Автор: SchrГ¶der Bernd
Название: Ordered Sets / An Introduction
ISBN: 0817641289 ISBN-13(EAN): 9780817641283
Издательство: Springer
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Описание: This work is an introduction to the basic tools of the theory of (partially) ordered sets such as visualization via diagrams, subsets, homomorphisms, important order-theoretical constructions, and classes of ordered sets. Using a thematic approach, the author presents open or recently solved problems to motivate the development of constructions and investigations for new classes of ordered sets. A wide range of material is presented, from classical results such as Dilworth's, Szpilrajn's and Hashimoto's Theorems to more recent results such as the Li--Milner Structure Theorem. Major topics covered include: chains and antichains, lowest upper and greatest lower bounds, retractions, lattices, the dimension of ordered sets, interval orders, lexicographic sums, products, enumeration, algorithmic approaches and the role of algebraic topology. Since there are few prerequisites, the text can be used as a focused follow-up or companion to a first proof (set theory and relations) or graph theory class. After working through a comparatively lean core, the reader can choose from a diverse range of topics such as structure theory, enumeration or algorithmic aspects. Also presented are some key topics less customary to discrete mathematics/graph theory, including a concise introduction to homology for graphs, and the presentation of forward checking as a more efficient alternative to the standard backtracking algorithm. The coverage throughout provides a solid foundation upon which research can be started by a mathematically mature reader. Rich in exercises, illustrations, and open problems, Ordered Sets: An Introduction is an excellent text for undergraduate and graduate students and a good resource for the interested researcher. Readers will discover order theory's role in discrete mathematics as a supplier of ideas as well as an attractive source of applications.

Автор: A.M. Glass; W.C. Holland
Название: Lattice-Ordered Groups
ISBN: 0792301161 ISBN-13(EAN): 9780792301165
Издательство: Springer
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Автор: Ma Jingjing
Название: Lecture Notes on Algebraic Structure of Lattice-Ordered Ring
ISBN: 9814571423 ISBN-13(EAN): 9789814571425
Издательство: World Scientific Publishing
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Описание: Algebraic Structure of Lattice-Ordered Rings presents an introduction to the theory of lattice-ordered rings and some new developments in this area in the last 10-15 years. It aims to provide the reader with a good foundation in the subject, as well as some new research ideas and topic in the field.This book may be used as a textbook for graduate and advanced undergraduate students who have completed an abstract algebra course including general topics on group, ring, module, and field. It is also suitable for readers with some background in abstract algebra and are interested in lattice-ordered rings to use as a self-study book.The book is largely self-contained, except in a few places, and contains about 200 exercises to assist the reader to better understand the text and practice some ideas.

Автор: Stuart A. Steinberg
Название: Lattice-ordered Rings and Modules
ISBN: 1489982973 ISBN-13(EAN): 9781489982971
Издательство: Springer
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Описание: This book provides an exposition of the algebraic aspects of the theory of lattice-ordered rings and lattice-ordered modules. All of the background material on rings, modules, and lattice-ordered groups necessary to make the work self-contained and accessible to a variety of readers is included. Key topics include: lattice-ordered groups, rings, and fields; Archimedean $l$-groups; f-rings and larger varieties of $l$-rings; the category of f-modules; various commutativity results. This text may be used as a textbook or for self-study by graduate students and researchers studying lattice-ordered rings and lattice-ordered modules.