Semimodular Lattices PDF Download
Are you looking for read ebook online? Search for your book and save it on your Kindle device, PC, phones or tablets. Download Semimodular Lattices PDF full book. Access full book title Semimodular Lattices by Manfred Stern. Download full books in PDF and EPUB format.
Author: Manfred Stern
Publisher: Cambridge University Press
ISBN: 0521461057
Category : Mathematics
Languages : en
Pages : 386
Get Book Here
Book Description
A survey of semimodularity that presents theory and applications in discrete mathematics, group theory and universal algebra.
Author: Manfred Stern
Publisher: Cambridge University Press
ISBN: 0521461057
Category : Mathematics
Languages : en
Pages : 386
Get Book Here
Book Description
A survey of semimodularity that presents theory and applications in discrete mathematics, group theory and universal algebra.
Author: George Grätzer
Publisher: Springer Science & Business Media
ISBN: 0817644628
Category : Mathematics
Languages : en
Pages : 287
Get Book Here
Book Description
Self-contained exposition presents the major results on congruence lattices of finite lattices Includes the latest findings from a pioneering researcher in the field Features the author's signature "Proof-by-Picture" method and its conversion to transparencies Contains complete proofs, an extensive bibliography and index, and nearly 80 open problems Excellent grad text and reference
Author: George Grätzer
Publisher: Springer
ISBN: 3319064134
Category : Mathematics
Languages : en
Pages : 472
Get Book Here
Book Description
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.
Author: G. Grätzer
Publisher: Birkhäuser
ISBN: 3034876335
Category : Science
Languages : en
Pages : 392
Get Book Here
Book Description
In the first half of the nineteenth century, George Boole's attempt to formalize propositional logic led to the concept of Boolean algebras. While investigating the axiomatics of Boolean algebras at the end of the nineteenth century, Charles S. Peirce and Ernst Schröder found it useful to introduce the lattice concept. Independently, Richard Dedekind's research on ideals of algebraic numbers led to the same discov ery. In fact, Dedekind also introduced modularity, a weakened form of distri butivity. Although some of the early results of these mathematicians and of Edward V. Huntington are very elegant and far from trivial, they did not attract the attention of the mathematical community. It was Garrett Birkhoff's work in the mid-thirties that started the general develop ment of lattice theory. In a brilliant series of papers he demonstrated the importance of lattice theory and showed that it provides a unifying framework for hitherto unrelated developments in many mathematical disciplines. Birkhoff himself, Valere Glivenko, Karl Menger, John von Neumann, Oystein Ore, and others had developed enough of this new field for Birkhoff to attempt to "seIl" it to the general mathematical community, which he did with astonishing success in the first edition of his Lattice Theory. The further development of the subject matter can best be followed by com paring the first, second, and third editions of his book (G. Birkhoff [1940], [1948], and [1967]).
Author: George Grätzer
Publisher: Springer Science & Business Media
ISBN: 9783764369965
Category : Mathematics
Languages : en
Pages : 688
Get Book Here
Book Description
"Grätzer’s 'General Lattice Theory' has become the lattice theorist’s bible. Now we have the second edition, in which the old testament is augmented by a new testament. The new testament gospel is provided by leading and acknowledged experts in their fields. This is an excellent and engaging second edition that will long remain a standard reference." --MATHEMATICAL REVIEWS
Author: Martin Aigner
Publisher: Springer Science & Business Media
ISBN: 3642591019
Category : Mathematics
Languages : en
Pages : 493
Get Book Here
Book Description
This book offers a well-organized, easy-to-follow introduction to combinatorial theory, with examples, notes and exercises. ". . . a very good introduction to combinatorics. This book can warmly be recommended first of all to students interested in combinatorics." Publicationes Mathematicae Debrecen
Author: Ezra Miller
Publisher: American Mathematical Soc.
ISBN: 9780821886953
Category : Mathematics
Languages : en
Pages : 710
Get Book Here
Book Description
Geometric combinatorics describes a wide area of mathematics that is primarily the study of geometric objects and their combinatorial structure. This text is a compilation of expository articles at the interface between combinatorics and geometry.
Author: L.N. Shevrin
Publisher: Springer Science & Business Media
ISBN: 9401587515
Category : Mathematics
Languages : en
Pages : 389
Get Book Here
Book Description
0.1. General remarks. For any algebraic system A, the set SubA of all subsystems of A partially ordered by inclusion forms a lattice. This is the subsystem lattice of A. (In certain cases, such as that of semigroups, in order to have the right always to say that SubA is a lattice, we have to treat the empty set as a subsystem.) The study of various inter-relationships between systems and their subsystem lattices is a rather large field of investigation developed over many years. This trend was formed first in group theory; basic relevant information up to the early seventies is contained in the book [Suz] and the surveys [K Pek St], [Sad 2], [Ar Sad], there is also a quite recent book [Schm 2]. As another inspiring source, one should point out a branch of mathematics to which the book [Baer] was devoted. One of the key objects of examination in this branch is the subspace lattice of a vector space over a skew field. A more general approach deals with modules and their submodule lattices. Examining subsystem lattices for the case of modules as well as for rings and algebras (both associative and non-associative, in particular, Lie algebras) began more than thirty years ago; there are results on this subject also for lattices, Boolean algebras and some other types of algebraic systems, both concrete and general. A lot of works including several surveys have been published here.
Author: George Grätzer
Publisher: Springer Science & Business Media
ISBN: 3034800185
Category : Mathematics
Languages : en
Pages : 639
Get Book Here
Book Description
This book started with Lattice Theory, First Concepts, in 1971. Then came General Lattice Theory, First Edition, in 1978, and the Second Edition twenty years later. Since the publication of the first edition in 1978, General Lattice Theory has become the authoritative introduction to lattice theory for graduate students and the standard reference for researchers. The First Edition set out to introduce and survey lattice theory. Some 12,000 papers have been published in the field since then; so Lattice Theory: Foundation focuses on introducing the field, laying the foundation for special topics and applications. Lattice Theory: Foundation, based on the previous three books, covers the fundamental concepts and results. The main topics are distributivity, congruences, constructions, modularity and semimodularity, varieties, and free products. The chapter on constructions is new, all the other chapters are revised and expanded versions from the earlier volumes. Almost 40 “diamond sections’’, many written by leading specialists in these fields, provide a brief glimpse into special topics beyond the basics. “Lattice theory has come a long way... For those who appreciate lattice theory, or who are curious about its techniques and intriguing internal problems, Professor Grätzer's lucid new book provides a most valuable guide to many recent developments. Even a cursory reading should provide those few who may still believe that lattice theory is superficial or naive, with convincing evidence of its technical depth and sophistication.” Bulletin of the American Mathematical Society “Grätzer’s book General Lattice Theory has become the lattice theorist’s bible.” Mathematical Reviews
Author: Richard Stanley
Publisher: Springer
ISBN: 1461597633
Category : Science
Languages : en
Pages : 317
Get Book Here
Book Description
