Lattices And Ordered Algebraic Structures

Author : T.S. Blyth
Publisher : Springer Science & Business Media
ISBN 13 : 1852339055
Total Pages : 311 pages
Book Rating : 4.50/5 ( download)

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Download or read book Lattices and Ordered Algebraic Structures written by T.S. Blyth and published by Springer Science & Business Media. This book was released on 2005-04-18 with total page 311 pages. Available in PDF, EPUB and Kindle. Book excerpt: "The text can serve as an introduction to fundamentals in the respective areas from a residuated-maps perspective and with an eye on coordinatization. The historical notes that are interspersed are also worth mentioning....The exposition is thorough and all proofs that the reviewer checked were highly polished....Overall, the book is a well-done introduction from a distinct point of view and with exposure to the author’s research expertise." --MATHEMATICAL REVIEWS

Author : W. Charles Holland
Publisher : CRC Press
ISBN 13 : 9789056993252
Total Pages : 214 pages
Book Rating : 4.59/5 ( download)

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Download or read book Ordered Algebraic Structures written by W. Charles Holland and published by CRC Press. This book was released on 2001-04-01 with total page 214 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is an outcome of the conference on ordered algebraic structures held at Nanjing. It covers a range of topics: lattice theory, ordered semi groups, partially ordered groups, totally ordered groups, lattice-ordered groups, and ordered fields.

Author : B. A. Davey
Publisher : Cambridge University Press
ISBN 13 : 9780521784511
Total Pages : 316 pages
Book Rating : 4.14/5 ( download)

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Download or read book Introduction to Lattices and Order written by B. A. Davey and published by Cambridge University Press. This book was released on 2002-04-18 with total page 316 pages. Available in PDF, EPUB and Kindle. Book excerpt: This new edition of Introduction to Lattices and Order presents a radical reorganization and updating, though its primary aim is unchanged. The explosive development of theoretical computer science in recent years has, in particular, influenced the book's evolution: a fresh treatment of fixpoints testifies to this and Galois connections now feature prominently. An early presentation of concept analysis gives both a concrete foundation for the subsequent theory of complete lattices and a glimpse of a methodology for data analysis that is of commercial value in social science. Classroom experience has led to numerous pedagogical improvements and many new exercises have been added. As before, exposure to elementary abstract algebra and the notation of set theory are the only prerequisites, making the book suitable for advanced undergraduates and beginning graduate students. It will also be a valuable resource for anyone who meets ordered structures.

Author : Jorge Martínez
Publisher : Springer Science & Business Media
ISBN 13 : 1475736274
Total Pages : 323 pages
Book Rating : 4.74/5 ( download)

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Download or read book Ordered Algebraic Structures written by Jorge Martínez and published by Springer Science & Business Media. This book was released on 2013-03-14 with total page 323 pages. Available in PDF, EPUB and Kindle. Book excerpt: From the 28th of February through the 3rd of March, 2001, the Department of Math ematics of the University of Florida hosted a conference on the many aspects of the field of Ordered Algebraic Structures. Officially, the title was "Conference on Lattice Ordered Groups and I-Rings", but its subject matter evolved beyond the limitations one might associate with such a label. This volume is officially the proceedings of that conference, although, likewise, it is more accurate to view it as a complement to that event. The conference was the fourth in wh at has turned into aseries of similar conferences, on Ordered Algebraic Structures, held in consecutive years. The first, held at the University of Florida in Spring, 1998, was a modest and informal affair. The fifth is in the final planning stages at this writing, for March 7-9, 2002, at Vanderbilt University. And although these events remain modest and reasonably informal, their scope has broadened, as they have succeeded in attracting mathematicians from other, related fields, as weIl as from more distant lands.

Author : Steven Roman
Publisher : Springer Science & Business Media
ISBN 13 : 0387789014
Total Pages : 307 pages
Book Rating : 4.19/5 ( download)

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Download or read book Lattices and Ordered Sets written by Steven Roman and published by Springer Science & Business Media. This book was released on 2008-12-15 with total page 307 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is intended to be a thorough introduction to the subject of order and lattices, with an emphasis on the latter. It can be used for a course at the graduate or advanced undergraduate level or for independent study. Prerequisites are kept to a minimum, but an introductory course in abstract algebra is highly recommended, since many of the examples are drawn from this area. This is a book on pure mathematics: I do not discuss the applications of lattice theory to physics, computer science or other disciplines. 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?FßÐE?FÑ?GßE?ÐF?GÑ and so on? In lattice-theoretic terms, this is the number of elements in the relatively free modular lattice on three generators. Dedekind [15] answered this question (the answer is #)) and wrote two papers on the subject of lattice theory, but then the subject lay relatively dormant until Garrett Birkhoff, Oystein Ore and others picked it up in the 1930s. Since then, many noted mathematicians have contributed to the subject, including Garrett Birkhoff, Richard Dedekind, Israel Gelfand, George Grätzer, Aleksandr Kurosh, Anatoly Malcev, Oystein Ore, Gian-Carlo Rota, Alfred Tarski and Johnny von Neumann.

Author : W. B. Powell
Publisher : CRC Press
ISBN 13 : 9780824773427
Total Pages : 220 pages
Book Rating : 4.2X/5 ( download)

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Download or read book Ordered Algebraic Structures written by W. B. Powell and published by CRC Press. This book was released on 1985-10-01 with total page 220 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Author : Laszlo Fuchs
Publisher : Courier Corporation
ISBN 13 : 0486173607
Total Pages : 240 pages
Book Rating : 4.03/5 ( download)

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Download or read book Partially Ordered Algebraic Systems written by Laszlo Fuchs and published by Courier Corporation. This book was released on 2014-03-05 with total page 240 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph by a distinguished mathematician constitutes the first systematic summary of research concerning partially ordered groups, semigroups, rings, and fields. The high-level, self-contained treatment features numerous problems. 1963 edition.

Author : T.S. Blyth
Publisher : Springer Science & Business Media
ISBN 13 : 184628127X
Total Pages : 311 pages
Book Rating : 4.73/5 ( download)

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Download or read book Lattices and Ordered Algebraic Structures written by T.S. Blyth and published by Springer Science & Business Media. This book was released on 2005-11-24 with total page 311 pages. Available in PDF, EPUB and Kindle. Book excerpt: "The text can serve as an introduction to fundamentals in the respective areas from a residuated-maps perspective and with an eye on coordinatization. The historical notes that are interspersed are also worth mentioning....The exposition is thorough and all proofs that the reviewer checked were highly polished....Overall, the book is a well-done introduction from a distinct point of view and with exposure to the author’s research expertise." --MATHEMATICAL REVIEWS

Author : Jingjing Ma
Publisher : World Scientific Publishing Company Incorporated
ISBN 13 : 9789814571425
Total Pages : 247 pages
Book Rating : 4.23/5 ( download)

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Download or read book Lecture Notes on Algebraic Structure of Lattice-ordered Rings written by Jingjing Ma and published by World Scientific Publishing Company Incorporated. This book was released on 2014 with total page 247 pages. Available in PDF, EPUB and Kindle. Book excerpt: Introduction to ordered algebraic systems. 1.1 Lattices. 1.2. Lattice-ordered groups and vector lattices. 1.3. Lattice-ordered rings and algebras -- 2. Lattice-ordered algebras with a d-basis. 2.1. Examples and basic properties. 2.2. Structure theorems -- 3. Positive derivations on l-rings. 3.1. Examples and basic properties. 3.2. f-ring and its generalizations. 3.3. Matrix l-rings. 3.4. Kernel of a positive derivation -- 4. Some topics on lattice-ordered rings. 4.1. Recognition of matrix l-rings with the entrywise order. 4.2. Positive cycles. 4.3. Nonzero f-elements in l-rings. 4.4. Quotient rings of lattice-ordered Ore domains. 4.5. Matrix l-algebras over totally ordered integral domains. 4.6. d-elements that are not positive. 4.7. Lattice-ordered triangular matrix algebras -- 5. l-ideals of l-unital lattice-ordered rings. 5.1. Maximal l-ideals. 5.2. l-ideals in commutative l-unital l-rings

Author : Nikolaos Galatos
Publisher : Elsevier
ISBN 13 : 0080489648
Total Pages : 532 pages
Book Rating : 4.43/5 ( download)

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Download or read book Residuated Lattices: An Algebraic Glimpse at Substructural Logics written by Nikolaos Galatos and published by Elsevier. This book was released on 2007-04-25 with total page 532 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book is meant to serve two purposes. The first and more obvious one is to present state of the art results in algebraic research into residuated structures related to substructural logics. The second, less obvious but equally important, is to provide a reasonably gentle introduction to algebraic logic. At the beginning, the second objective is predominant. Thus, in the first few chapters the reader will find a primer of universal algebra for logicians, a crash course in nonclassical logics for algebraists, an introduction to residuated structures, an outline of Gentzen-style calculi as well as some titbits of proof theory - the celebrated Hauptsatz, or cut elimination theorem, among them. These lead naturally to a discussion of interconnections between logic and algebra, where we try to demonstrate how they form two sides of the same coin. We envisage that the initial chapters could be used as a textbook for a graduate course, perhaps entitled Algebra and Substructural Logics. As the book progresses the first objective gains predominance over the second. Although the precise point of equilibrium would be difficult to specify, it is safe to say that we enter the technical part with the discussion of various completions of residuated structures. These include Dedekind-McNeille completions and canonical extensions. Completions are used later in investigating several finiteness properties such as the finite model property, generation of varieties by their finite members, and finite embeddability. The algebraic analysis of cut elimination that follows, also takes recourse to completions. Decidability of logics, equational and quasi-equational theories comes next, where we show how proof theoretical methods like cut elimination are preferable for small logics/theories, but semantic tools like Rabin's theorem work better for big ones. Then we turn to Glivenko's theorem, which says that a formula is an intuitionistic tautology if and only if its double negation is a classical one. We generalise it to the substructural setting, identifying for each substructural logic its Glivenko equivalence class with smallest and largest element. This is also where we begin investigating lattices of logics and varieties, rather than particular examples. We continue in this vein by presenting a number of results concerning minimal varieties/maximal logics. A typical theorem there says that for some given well-known variety its subvariety lattice has precisely such-and-such number of minimal members (where values for such-and-such include, but are not limited to, continuum, countably many and two). In the last two chapters we focus on the lattice of varieties corresponding to logics without contraction. In one we prove a negative result: that there are no nontrivial splittings in that variety. In the other, we prove a positive one: that semisimple varieties coincide with discriminator ones. Within the second, more technical part of the book another transition process may be traced. Namely, we begin with logically inclined technicalities and end with algebraically inclined ones. Here, perhaps, algebraic rendering of Glivenko theorems marks the equilibrium point, at least in the sense that finiteness properties, decidability and Glivenko theorems are of clear interest to logicians, whereas semisimplicity and discriminator varieties are universal algebra par exellence. It is for the reader to judge whether we succeeded in weaving these threads into a seamless fabric.