Download or read book Ring Lattice and Geometric Extensions of Boolean Theory written by Nadimpalli Venkata Subrahmanyam and published by . This book was released on 1962 with total page 338 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Commutative Idempotent Generated Rings as Generalized Boolean Rings written by Martin Kenneth McCrea and published by . This book was released on 1972 with total page 126 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Lattice Functions and Equations written by Sergiu Rudeanu and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 442 pages. Available in PDF, EPUB and Kindle. Book excerpt: One of the chief aims of this self-contained monograph is to survey recent developments of Boolean functions and equations, as well as lattice functions and equations in more general classes of lattices. 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. Special attention is also paid to consistency conditions and reproductive general solutions. Applications refer to graph theory, automata theory, synthesis of circuits, fault detection, databases, marketing and others. Lattice Functions and Equations updates and extends the author's previous monograph - Boolean Functions and Equations.
Download or read book Algebra and Geometry written by R. V. Gamkrelidze and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 259 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains five review articles, three in the Al gebra part and two in the Geometry part, surveying the fields of ring theory, modules, and lattice theory in the former, and those of integral geometry and differential-geometric methods in the calculus of variations in the latter. The literature covered is primarily that published in 1965-1968. v CONTENTS ALGEBRA RING THEORY L. A. Bokut', K. A. Zhevlakov, and E. N. Kuz'min § 1. Associative Rings. . . . . . . . . . . . . . . . . . . . 3 § 2. Lie Algebras and Their Generalizations. . . . . . . 13 ~ 3. Alternative and Jordan Rings. . . . . . . . . . . . . . . . 18 Bibliography. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25 MODULES A. V. Mikhalev and L. A. Skornyakov § 1. Radicals. . . . . . . . . . . . . . . . . . . 59 § 2. Projection, Injection, etc. . . . . . . . . . . . . . . . . . . 62 § 3. Homological Classification of Rings. . . . . . . . . . . . 66 § 4. Quasi-Frobenius Rings and Their Generalizations. . 71 § 5. Some Aspects of Homological Algebra . . . . . . . . . . 75 § 6. Endomorphism Rings . . . . . . . . . . . . . . . . . . . . . 83 § 7. Other Aspects. . . . . . . . . . . . . . . . . . . 87 Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . , 91 LATTICE THEORY M. M. Glukhov, 1. V. Stelletskii, and T. S. Fofanova § 1. Boolean Algebras . . . . . . . . . . . . . . . . . . . . . " 111 § 2. Identity and Defining Relations in Lattices . . . . . . 120 § 3. Distributive Lattices. . . . . . . . . . . . . . . . . . . . . 122 vii viii CONTENTS § 4. Geometrical Aspects and the Related Investigations. . . . . . . . . . . . • . . • . . . . . . . . . • 125 § 5. Homological Aspects. . . . . . . . . . . . . . . . . . . . . . 129 § 6. Lattices of Congruences and of Ideals of a Lattice . . 133 § 7. Lattices of Subsets, of Subalgebras, etc. . . . . . . . . 134 § 8. Closure Operators . . . . . . . . . . . . . . . . . . . . . . . 136 § 9. Topological Aspects. . . . . . . . . . . . . . . . . . . . . . 137 § 10. Partially-Ordered Sets. . . . . . . . . . . . . . . . . . . . 141 § 11. Other Questions. . . . . . . . . . . . . . . . . . . . . . . . . 146 Bibliography. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 148 GEOMETRY INTEGRAL GEOMETRY G. 1. Drinfel'd Preface . . . . . . . . .
Download or read book Summary of the Dissertation s Submitted in Partial Satisfaction of the Requirements for the Degree of Doctor of Philosophy written by University of California (System). Graduate Division and published by . This book was released on 1962-06 with total page 608 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book An Introduction to Abstract Algebra written by F. M. Hall and published by CUP Archive. This book was released on 1966 with total page 404 pages. Available in PDF, EPUB and Kindle. Book excerpt: A summary of basic group theory is followed by accounts of group homomorphisms, rings, fields and integral domains. The book is intended both for those who wish to know something about modern algebra and also for those already familiar with the elements of the subject who wish to study further.
Download or read book Commencement Programs written by University of California, Berkeley and published by . This book was released on 1962 with total page 1032 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Library of Congress Subject Headings written by Library of Congress and published by . This book was released on 2006 with total page 1942 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Summary of the Dissertation Submitted in Partial Satisfaction of the Requirements for the Degree of Doctor of Philosophy written by University of California, Berkeley. Graduate Division and published by . This book was released on 1962 with total page 608 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book The New Era in American Mathematics 1920 1950 written by Karen Hunger Parshall and published by Princeton University Press. This book was released on 2022-02-22 with total page 640 pages. Available in PDF, EPUB and Kindle. Book excerpt: A meticulously researched history on the development of American mathematics in the three decades following World War I As the Roaring Twenties lurched into the Great Depression, to be followed by the scourge of Nazi Germany and World War II, American mathematicians pursued their research, positioned themselves collectively within American science, and rose to global mathematical hegemony. How did they do it? The New Era in American Mathematics, 1920–1950 explores the institutional, financial, social, and political forces that shaped and supported this community in the first half of the twentieth century. In doing so, Karen Hunger Parshall debunks the widely held view that American mathematics only thrived after European émigrés fled to the shores of the United States. Drawing from extensive archival and primary-source research, Parshall uncovers the key players in American mathematics who worked together to effect change and she looks at their research output over the course of three decades. She highlights the educational, professional, philanthropic, and governmental entities that bolstered progress. And she uncovers the strategies implemented by American mathematicians in their quest for the advancement of knowledge. Throughout, she considers how geopolitical circumstances shifted the course of the discipline. Examining how the American mathematical community asserted itself on the international stage, The New Era in American Mathematics, 1920–1950 shows the way one nation became the focal point for the field.
Download or read book Library of Congress Subject Headings written by Library of Congress. Cataloging Policy and Support Office and published by . This book was released on 2001 with total page 1614 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book American Doctoral Dissertations written by and published by . This book was released on 1988 with total page 728 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Geometry of Quantum Theory written by V.S. Varadarajan and published by Springer Science & Business Media. This book was released on 2007-12-03 with total page 426 pages. Available in PDF, EPUB and Kindle. Book excerpt: Available for the first time in soft cover, this book is a classic on the foundations of quantum theory. It examines the subject from a point of view that goes back to Heisenberg and Dirac and whose definitive mathematical formulation is due to von Neumann. This view leads most naturally to the fundamental questions that are at the basis of all attempts to understand the world of atomic and subatomic particles.
Download or read book Encyclopaedia of Mathematics written by Michiel Hazewinkel and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 595 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the first Supplementary volume to Kluwer's highly acclaimed Encyclopaedia of Mathematics. This additional volume contains nearly 600 new entries written by experts and covers developments and topics not included in the already published 10-volume set. These entries have been arranged alphabetically throughout. A detailed index is included in the book. This Supplementary volume enhances the existing 10-volume set. Together, these eleven volumes represent the most authoritative, comprehensive up-to-date Encyclopaedia of Mathematics available.
Download or read book Extensions of Rings and Modules written by Gary F. Birkenmeier and published by Springer Science & Business Media. This book was released on 2013-07-19 with total page 442 pages. Available in PDF, EPUB and Kindle. Book excerpt: The "extensions" of rings and modules have yet to be explored in detail in a research monograph. This book presents state of the art research and also stimulating new and further research. Broken into three parts, Part I begins with basic notions, terminology, definitions and a description of the classes of rings and modules. Part II considers the transference of conditions between a base ring or module and its extensions. And Part III utilizes the concept of a minimal essental extension with respect to a specific class (a hull). Mathematical interdisciplinary applications appear throughout. Major applications of the ring and module theory to Functional Analysis, especially C*-algebras, appear in Part III, make this book of interest to Algebra and Functional Analysis researchers. Notes and exercises at the end of every chapter, and open problems at the end of all three parts, lend this as an ideal textbook for graduate or advanced undergradate students.
Download or read book Boolean Algebras written by Roman Sikorski and published by Springer. This book was released on 2013-04-17 with total page 184 pages. Available in PDF, EPUB and Kindle. Book excerpt: There are two aspects in the theory of Boolean algebras: algebraic and set-theoretical. Boolean algebras can be considered as a special kind of algebraic rings, or as a generalization of the set-theoretical notion of field of sets. Fundamental theorems in the both directions are due to M. H. STONE whose papers have opened a new period in the development of the theory. This work treats of the set-theoretical aspect, the algebraic one being scarcely mentioned. The book is composed of two Chapters and an Appendix. Chapter I is devoted to the study of Boolean algebras from the point of view of finite Boolean operations only. A greater part of its contents can be found also in the books of BIRKHOFF [2J and HERMES [1 J. Chapter II seems to be the first systematic study of Boolean algebras with infinite Boolean operations. To understand Chapters land II it suffices to know only fundamental notions from General Set Theory and Set-theoretical Topology. No knowledge of Lattice Theory or Abstract Algebra is supposed. Less known topological theorems are recalled. Only a few examples use more advanced topological means but they can be omitted. All theorems in both Chapters are given with full proofs. On the contrary, no complete proofs are given in the Appendix which contains mainly a short exposition of applications of Boolean algebras to other parts of Mathematics with references to the literature. An elementary knowledge of discussed theories is supposed.
Download or read book Notices of the American Mathematical Society written by American Mathematical Society and published by . This book was released on 1977 with total page 628 pages. Available in PDF, EPUB and Kindle. Book excerpt: Contains articles of significant interest to mathematicians, including reports on current mathematical research.
