Монография. — М.: Наука, Главная редакция физико-математической литературы, 1984. — 128 с. — (Современная алгебра). Известно, что класс решеток с единственными дополнениями содержит все булевы решетки, но не сводится к ним. Однако до сих пор не указан явный пример небулевой решетки из этого класса. Нет ответа и на вопрос о том, существуют ли в нем полные небулевы решетки. Книга...
Cambridge: Cambridge University Press, 2024. — 367 p. — (Cambridge Tracts in Theoretical Computer Science, 61). — ISBN: 1009349694. Introducing Stone – Priestley duality theory and its applications to logic and theoretical computer science, this book equips graduate students and researchers with the theoretical background necessary for reading and understanding current research...
М.: Наука, Главная редакция физико-математической литературы, 1970. — 148 с. Настоящее руководство адресовано тем математикам, которые хотят ознакомиться с основами теории структур, хотя еще (или уже!) не избрали эту ветвь алгебры своей специальностью. Поэтому при отборе результатов предпочтение отдавалось тем из них, которые или способствуют выработке теоретико-структурного...
Springer Basel AG, 2011. — 639 p. — ISBN 978-3-0348-0017-4. 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...
3rd ed. — Birkhäuser, 2023. — 439 p. — ISBN 3031290623. The congruences of a lattice form the congruence lattice. Over the last several decades, the study of congruence lattices has established itself as a large and important field with a great number of interesting and deep results , as well as many open problems. Written by one of the leading experts in lattice theory , this...
Cham: Springer, 2022. — 293 p. This book addresses Birkhoff and Mal'cev's problem of describing subquasivariety lattices. The text begins by developing the basics of atomic theories and implicational theories in languages that may, or may not, contain equality. Subquasivariety lattices are represented as lattices of closed algebraic subsets of a lattice with operators, which...
2nd Edition. — Cambridge University Press, 2002. — 312 p. — ISBN-1 9780521784511. Ordered structures have been increasingly recognized in recent years due to an explosion of interest in theoretical computer science and all areas of discrete mathematics. This book covers areas such as ordered sets and lattices. A key feature of ordered sets, one which is emphasized in the text,...
Boca Raton: CRC Press, 2022. — 432 p. Lattice theory extends into virtually every branch of mathematics, ranging from measure theory and convex geometry to probability theory and topology. A more recent development has been the rapid escalation of employing lattice theory for various applications outside the domain of pure mathematics. These applications range from electronic...
CRC Press, 2022. — 432 p. — ISBN 9780367722951. Lattice theory extends into virtually every branch of mathematics, ranging from measure theory and convex geometry to probability theory and topology. A more recent development has been the rapid escalation of employing lattice theory for various applications outside the domain of pure mathematics. These applications range from...
Cambridge: Cambridge University Press, 1999. — 385 p. — (Encyclopedia of Mathematics and its Applications 73). — ISBN: 978-0-521-46105-4. Lattice theory evolved as part of algebra in the nineteenth century through the work of Boole, Peirce and Schr?der, and in the first half of the twentieth century through the work of Dedekind, Birkhoff, Ore, von Neumann, Mac Lane, Wilcox,...
Cambridge: Cambridge University Press, 1999. — 385 p. — (Encyclopedia of Mathematics and its Applications 73). — ISBN: 978-0-521-46105-4. Lattice theory evolved as part of algebra in the nineteenth century through the work of Boole, Peirce and Schr?der, and in the first half of the twentieth century through the work of Dedekind, Birkhoff, Ore, von Neumann, Mac Lane, Wilcox,...
Harvard University, 2009. — 96 p. — (Honors thesis at Harvard University). Vector PDF We present an exposition of weighted theta functions, which are weighted generating functions for the norms and distribution of lattice vectors. We derive a decomposition theorem for the space of degree-d homogeneous polynomials in terms of spaces of harmonic polynomials and then prove that the...
Berlin: Heldermann Verlag, 1995. — 274 p. Laudatio G. Birkhoff: Lattices and their applications M. K. Bennett: Lattices and geometry R. Freese: New results on free lattices R. Freese, K. Kearnes, J. B. Nation: Congruence lattices of ongruence semidistributive algebras B. Ganter: Lattice theory and formal concept analysis - a subjective introduction G. Gratzer, E. T. Schmidt:...
Springer, 2018. — 343 p. — (Developments in Mathematics 54). — ISBN: 978-3-319-78947-7. This monograph provides a modern introduction to the theory of quantales. First coined by C.J. Mulvey in 1986, quantales have since developed into a significant topic at the crossroads of algebra and logic, of notable interest to theoretical computer science. This book recasts the subject...
Cambridge University Press, UK, 2013. — 390 p. — (Encyclopedia of Mathematics and Its Applications 150) — ISBN: 1107039908. The study of lattice sums is an important topic in mathematics, physics, and other areas of science. It is not a new field, dating back at least to the work of Appell in 1884, and has attracted contributions from some of the most eminent practitioners of...
London: Springer, 2001. — 441 p. Lattice (Boolean) functions are algebraic functions defined over an arbitrary lattice (Boolean algebra), while lattice (Boolean) equations are equations expressed in terms of lattice (Boolean) functions. This self-contained monograph surveys recent developments of Boolean functions and equations, as well as lattice functions and equations in...
Springer International Publishing, Switzerland, 2016. — 625 p. — ISBN: 331944235X. 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...
2nd Edition. — Springer International Publishing, Switzerland, 2016. — 361 p. — ISBN: 9783319387963 This is a self-contained exposition by one of the leading experts in lattice theory, George Grätzer, presenting the major results of the last 70 years on congruence lattices of finite lattices, featuring the author's signature Proof-by-Picture method. Key features * Insightful...
Springer Science+Business Media, LLC, 2008. — 307 p. — ISBN: 9780387789002 This book is intended to be a thorough introduction to the subject of ordered sets 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...
М., 2013. — 221 с. Главными инструментами математической кибернетики являются дискретная математика и алгебра. Основные понятия и свойства математических структур этих наук - частично упорядоченные множества, решетки, булевы алгебры, алгебраические системы - являются рабочим инструментом ученых в различных областях прикладной математики (распознавание образов и прогнозирование,...
Springer Netherlands, 1988. — 204 p. — (Reidel Texts in the Mathematical Sciences 4). — ISBN: 978-94-010-7792-7 (Print) 978-94-009-2871-8 (Online).
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...
3rd Ed. — NY.: American Mathematical Society, 1967. — 418 p. [1st Ed., 1940; 2nd (Revised) Ed., 1948], English. Interactive menu. ( OCR-слой ). Preface to the Third Edition. The purpose of this edition is threefold: to make the deeper ideas of lattice theory accessible to mathematicians generally, to portray its structure, and to indicate some of its most interesting...
2nd (Revised) Ed. — NY.: American Mathematical Society, 1948. — 291 p. (1st Ed., 1940), English. Preface to the second Edition. The development of lattice theory may be divided into three stages. First, follOwing the publication in 1847 of Boole's "Mathematical Analysis of Logic," various mathematical logicians made postulational analyses of Boolean algebra and the algebra of...
Published online. — 143 p. (Revised Notes on Lattice Theory - first eleven chapters). English. [University of Hawaii]. In the early 1890's, Richard Dedekind was working on a revised and enlarged edition of Dirichlet'sVorlesungen ¨uber Zahlentheorie, and asked himself the following question: Given three subgroupsA, B, Cof an abelian groupG, how many di erent subgroups can you...
NY.: Ithaca, Cornell University Library, 2014. — 28 p. English. { Free Published : Cornell University Library (arXiv:1308.4495v2 [math.RA] 15 Jan 2014)}. [Submitted on 21 Aug 2013 (v1), last revised 15 Jan 2014 (this version, v2)]. This paper provides a fresh perspective on the representation of distributive bilattices and of related varieties. The techniques of naturalduality...
Second edition. — Cambridge University Press. — ISBN: 978-0-521-78451-1. This new edition of Introduction to Lattices and Order is substantially different from the original one published in 1990. We believe that the revision greatly enhances the book's usefulness and topicality. Our overall aims however remains the same: to provide a textbook introduction which shows the...
D. Reidel Publishing Company, 1985. — 394 p. Growing specialization and diversification have brought a host of monographs and textbooks on increasingly specialized topics. Bow ever, the "tree" of knowledge of mathematics and related fields does not grow only by putting forth new branches. It also happens, quite often in fact, that branches which were thought to be completely...
Basel: Birkhäuser, 2014. — 468 p. 78 illus. 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...
Springer, 2011 – 644 p.
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...
Учебное пособие. — Казань: Казанский (Приволжский) федеральный университет (КФУ), 2012. — 74 с. Данное пособие предназначено для проведения занятий со студентами младших и старших курсов, специализирующихся в области алгебры, функционального анализа и топологии. Форма проведения может быть разной: спецкурс, курс по выбору или факультативный курс. Пособие может быть полезно при...
Монография. — Пер. с англ. А.Д. Больбота, В.А. Горбунова, В.И. Туманова. — Под ред. Д.М. Смирнова.— М.: Мир, 1982. — 456 с. Современная монография по теории решеток - одному из направлений алгебры, имеющему глубокие связи с различными областями математики. Содержит большое количество упражнений разной трудности, а также около 200 открытых проблем. Включен новый материал,...
Перев. с англ. М.И. Граева. — М.: Иностранная литература, 1952. — 407 с. Теория структур — молодая ветвь математики, оформившаяся в качестве самостоятельной научной дисциплины менее двадцати лет тому назад. Даже само основное понятие, которое является предметом изучения этой теории, еще не имеет общепринятого названия - в американской литературе преимущественно употребляется...
Перев. с англ. В.Н. Салий. — Под ред. Л.А. Скорнякова. — М.: Наука, Главная редакция физико-математической литературы, 1984. — 568 с. Книга является энциклопедией классической теории решеток. В ней отражены основные направления этой теории, развивавшиеся в первые десятилетия ее становления. Большую роль в развитии теории решеток сыграли проблемы Биркгофа - некоторые из них...
Уважаемые: Администратор, модераторы и доверенные пользователи.Друзья, я глубоко и сердечно благодарен Вам за создание подраздела Теория решёток, раздела Общая алгебра. Теперь людям гораздо легче будет ориентироваться в разделе Общая Алгебра и быстрее искать нужную литературу. Слава Богу! Да благословит Господь наш сайт, а также Вас, ваших родных, близких, друзей и знакомых. С уважением, благодарностью и благословением,
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Теперь людям гораздо легче будет ориентироваться в разделе Общая Алгебра и быстрее искать нужную литературу. Слава Богу!
Да благословит Господь наш сайт, а также Вас, ваших родных, близких, друзей и знакомых.
С уважением, благодарностью и благословением,