Download or read book Polyadic Groups written by Wieslaw A. Dudek and published by CRC Press. This book was released on 2024-03-22 with total page 424 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a general, unified approach to the theory of polyadic groups, their normal subgroups and matrix representations. The author focuses on those properties of polyadic groups which are not present in the binary case. These properties indicate a strong relationship between polyadic groups and various group-like algebras, as well as ternary Hopf algebras and n-Lie algebras that are widely used in theoretical physics. The relationships of polyadic groups with special types of binary groups, called covering groups and binary retracts, are described. These relationships allow the study of polyadic groups using these binary groups and their automorphisms. The book also describes the affine geometry induced by polyadic groups and fuzzy subsets defined on polyadic groups. Finally, we discuss the categories of polyadic groups and the relationships between the different varieties of polyadic groups. In many cases, we give elegant new proofs of known theorems. We also give many interesting examples and applications. The book contains many little-known results from articles previously published in hard-to-reach Russian, Ukrainian and Macedonian journals. These articles are not in English.
Download or read book Discussiones Mathematicae written by and published by . This book was released on 2006 with total page 568 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Universal and Applied Algebra written by Katarzyna Hałkowska and published by World Scientific Publishing Company. This book was released on 1989 with total page 412 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book General Algebra 1988 written by Wilfried Nöbauer and published by North Holland. This book was released on 1990 with total page 278 pages. Available in PDF, EPUB and Kindle. Book excerpt: At the beginning of 1988, the Austrian mathematical community was preparing to celebrate the sixtieth birthday of one of its outstanding members, Wilfried Nobauer, professor at Vienna Technical University. An international conference on general algebra was planned to celebrate this jubilee. However, Professor Nobauer's untimely death, just six months before the conference, turned the conference into a memorial event. Eighty-three algebraists from twenty-one countries met in Krems to present and discuss their work. This volume reflects the research being carried out in various branches of algebra throughout the world.
Download or read book Referativny zhurnal written by and published by . This book was released on 1987 with total page 632 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Mathematical Reviews written by and published by . This book was released on 1999 with total page 774 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Algebraic Logic written by Paul R. Halmos and published by Courier Dover Publications. This book was released on 2016-01-18 with total page 276 pages. Available in PDF, EPUB and Kindle. Book excerpt: Originally published: New York: Chelsea Publishing Company, 1962.
Download or read book Sets for Mathematics written by F. William Lawvere and published by Cambridge University Press. This book was released on 2003-01-27 with total page 280 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this book, first published in 2003, categorical algebra is used to build a foundation for the study of geometry, analysis, and algebra.
Download or read book Solvability Provability Definability written by Emil Leon Post and published by Birkhauser. This book was released on 1994 with total page 592 pages. Available in PDF, EPUB and Kindle. Book excerpt: Emil Post was a pioneer of 20th century mathematical logic whose influence on computer science is particularly remarkable considering his lack of any contact with computing machines. Post's approach, revolutionary for the time, was to study logical systems from the outside, using ordinary mathematical methods. His investigations led him to set forth what has become the standard paradigm for studying logical systems. By showing how a system of logic could be viewed as a kind of general combinatorial system, Post provided the basis for much of modern computer science. No index. Annotation copyright by Book News, Inc., Portland, OR
Download or read book The Higher Infinite written by Akihiro Kanamori and published by Springer Science & Business Media. This book was released on 2008-11-23 with total page 555 pages. Available in PDF, EPUB and Kindle. Book excerpt: Over the years, this book has become a standard reference and guide in the set theory community. It provides a comprehensive account of the theory of large cardinals from its beginnings and some of the direct outgrowths leading to the frontiers of contemporary research, with open questions and speculations throughout.
Download or read book Polyadic Algebraic Structures written by Steven Duplij and published by . This book was released on 2022 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book is devoted to the thorough study of polyadic (higher arity) algebraic structures, which has a long history, starting from 19th century. The main idea was to take a single set, closed under one binary operation, and to 'generalize' it by increasing the arity of the operation, called a polyadic operation. Until now, a general approach to polyadic concrete many-set algebraic structures was absent. We propose to investigate algebraic structures in the 'concrete way' and provide consequent 'polyadization' of each operation, starting from group-like structures and finishing with the Hopf algebra structures. Polyadic analogs of homomorphisms which change arity, heteromorphisms, are introduced and applied for constructing unusual representations, multiactions, matrix representations and polyadic analogs of direct product. We provide the polyadic generalization of the Yang-Baxter equation, find its constant solutions, and introduce polyadic tensor categories.
Download or read book N ary structures written by Blagoj Popov and published by . This book was released on 1982 with total page 310 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Bibliographie internationale annuelle des m langes written by and published by . This book was released on 1987 with total page 730 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Introduction to Mathematical Logic written by Elliot Mendelsohn and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 351 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a compact mtroduction to some of the pnncipal tOpICS of mathematical logic . In the belief that beginners should be exposed to the most natural and easiest proofs, I have used free-swinging set-theoretic methods. The significance of a demand for constructive proofs can be evaluated only after a certain amount of experience with mathematical logic has been obtained. If we are to be expelled from "Cantor's paradise" (as nonconstructive set theory was called by Hilbert), at least we should know what we are missing. The major changes in this new edition are the following. (1) In Chapter 5, Effective Computability, Turing-computabIlity IS now the central notion, and diagrams (flow-charts) are used to construct Turing machines. There are also treatments of Markov algorithms, Herbrand-Godel-computability, register machines, and random access machines. Recursion theory is gone into a little more deeply, including the s-m-n theorem, the recursion theorem, and Rice's Theorem. (2) The proofs of the Incompleteness Theorems are now based upon the Diagonalization Lemma. Lob's Theorem and its connection with Godel's Second Theorem are also studied. (3) In Chapter 2, Quantification Theory, Henkin's proof of the completeness theorem has been postponed until the reader has gained more experience in proof techniques. The exposition of the proof itself has been improved by breaking it down into smaller pieces and using the notion of a scapegoat theory. There is also an entirely new section on semantic trees.
Download or read book An Introduction to Ramsey Theory written by Matthew Katz and published by American Mathematical Soc.. This book was released on 2018-10-03 with total page 224 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book takes the reader on a journey through Ramsey theory, from graph theory and combinatorics to set theory to logic and metamathematics. Written in an informal style with few requisites, it develops two basic principles of Ramsey theory: many combinatorial properties persist under partitions, but to witness this persistence, one has to start with very large objects. The interplay between those two principles not only produces beautiful theorems but also touches the very foundations of mathematics. In the course of this book, the reader will learn about both aspects. Among the topics explored are Ramsey's theorem for graphs and hypergraphs, van der Waerden's theorem on arithmetic progressions, infinite ordinals and cardinals, fast growing functions, logic and provability, Gödel incompleteness, and the Paris-Harrington theorem. Quoting from the book, “There seems to be a murky abyss lurking at the bottom of mathematics. While in many ways we cannot hope to reach solid ground, mathematicians have built impressive ladders that let us explore the depths of this abyss and marvel at the limits and at the power of mathematical reasoning at the same time. Ramsey theory is one of those ladders.”
Download or read book The New Elements of Mathematics Mathematical miscellanea 2 v written by Charles Sanders Peirce and published by . This book was released on 1976 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
