Non Associative Algebraic Structures Using Finite Complex Numbers
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Non Associative Algebraic Structures Using Finite Complex Numbers
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Author : W.B. Vasantha Kandasamy, Florentin Smarandache
language : en
Publisher: Infinite Study
Release Date : 2012
Non Associative Algebraic Structures Using Finite Complex Numbers written by W.B. Vasantha Kandasamy, Florentin Smarandache and has been published by Infinite Study this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012 with Mathematics categories.
The authors have used the concept of finite complex modulo integers to construct non associative algebraic structures like groupoids, loops and quasi-loops.Using these structures we built non associative complex matrix groupoids and complex polynomial groupoids.The authors suggest over 300 problems and some are at the research level.
Complex Numbers
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Author : Wilfred Halliday Cockcroft
language : en
Publisher:
Release Date : 1972
Complex Numbers written by Wilfred Halliday Cockcroft and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1972 with Mathematics categories.
Non Associative Algebraic Structures On Mod Planes
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Author : W. B. Vasantha Kandasamy
language : en
Publisher: Infinite Study
Release Date : 2015
Non Associative Algebraic Structures On Mod Planes written by W. B. Vasantha Kandasamy and has been published by Infinite Study this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015 with Algebras, Linear categories.
In this book authors for the first time construct non-associative algebraic structures on the MOD planes. Using MOD planes we can construct infinite number of groupoids for a fixed m and all these MOD groupoids are of infinite cardinality. Special identities satisfied by these MOD groupoids build using the six types of MOD planes are studied. Further, the new concept of special pseudo zero of these groupoids are defined, described and developed. Also conditions for these MOD groupoids to have special elements like idempotent, special pseudo zero divisors and special pseudo nilpotent are obtained. Further non-associative MOD rings are constructed using MOD groupoids and commutative rings with unit. That is the MOD groupoid rings gives infinitely many non-associative ring. These rings are analysed for substructures and special elements. This study is new and innovative and several open problems are suggested.
The Encyclopedia Of Neutrosophic Researchers Vol I
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Author : Florentin Smarandache
language : en
Publisher: Infinite Study
Release Date : 2016-11-12
The Encyclopedia Of Neutrosophic Researchers Vol I written by Florentin Smarandache and has been published by Infinite Study this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-11-12 with Mathematics categories.
This is the first volume of the Encyclopedia of Neutrosophic Researchers, edited from materials offered by the authors who responded to the editor’s invitation. The 78 authors are listed alphabetically. The introduction contains a short history of neutrosophics, together with links to the main papers and books. Neutrosophic set, neutrosophic logic, neutrosophic probability, neutrosophic statistics, neutrosophic measure, neutrosophic precalculus, neutrosophic calculus and so on are gaining significant attention in solving many real life problems that involve uncertainty, impreciseness, vagueness, incompleteness, inconsistent, and indeterminacy. In the past years the fields of neutrosophics have been extended and applied in various fields, such as: artificial intelligence, data mining, soft computing, decision making in incomplete / indeterminate / inconsistent information systems, image processing, computational modelling, robotics, medical diagnosis, biomedical engineering, investment problems, economic forecasting, social science, humanistic and practical achievements.
Exploring The Extension Of Natural Operations On Intervals Matrices And Complex Numbers
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Author : W. B. Vasantha Kandasamy, Florentin Smarandache
language : en
Publisher: Infinite Study
Release Date : 2012
Exploring The Extension Of Natural Operations On Intervals Matrices And Complex Numbers written by W. B. Vasantha Kandasamy, Florentin Smarandache and has been published by Infinite Study this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012 with Algebra categories.
In this book we explore the possibility of extending the natural operations on reals to intervals and matrices. The extension to intervals makes us define a natural class of intervals in which we accept [a, b], a greater than b. Further, we introduce a complex modulo integer in Z_n (n, a positive integer) and denote it by iF with iF^2 = n-1.
Smarandache Special Elements In Multiset Semigroups
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Author : W. B. Vasantha Kandasamy
language : en
Publisher: Infinite Study
Release Date :
Smarandache Special Elements In Multiset Semigroups written by W. B. Vasantha Kandasamy and has been published by Infinite Study this book supported file pdf, txt, epub, kindle and other format this book has been release on with Mathematics categories.
Authors in this book study the notion of Smarandache element in multiset semigroups. It is important to keep on record that we define four operations on multisets viz. +, X, union and intersection in a free way. Thus all sets finite or infinite order contribute to infinite order multisets and the semigroup under any of these operations is of infinite order.
Algebra And Number Theory
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Author : Martyn R. Dixon
language : en
Publisher: John Wiley & Sons
Release Date : 2011-07-15
Algebra And Number Theory written by Martyn R. Dixon and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-07-15 with Mathematics categories.
Explore the main algebraic structures and number systems that play a central role across the field of mathematics Algebra and number theory are two powerful branches of modern mathematics at the forefront of current mathematical research, and each plays an increasingly significant role in different branches of mathematics, from geometry and topology to computing and communications. Based on the authors' extensive experience within the field, Algebra and Number Theory has an innovative approach that integrates three disciplines—linear algebra, abstract algebra, and number theory—into one comprehensive and fluid presentation, facilitating a deeper understanding of the topic and improving readers' retention of the main concepts. The book begins with an introduction to the elements of set theory. Next, the authors discuss matrices, determinants, and elements of field theory, including preliminary information related to integers and complex numbers. Subsequent chapters explore key ideas relating to linear algebra such as vector spaces, linear mapping, and bilinear forms. The book explores the development of the main ideas of algebraic structures and concludes with applications of algebraic ideas to number theory. Interesting applications are provided throughout to demonstrate the relevance of the discussed concepts. In addition, chapter exercises allow readers to test their comprehension of the presented material. Algebra and Number Theory is an excellent book for courses on linear algebra, abstract algebra, and number theory at the upper-undergraduate level. It is also a valuable reference for researchers working in different fields of mathematics, computer science, and engineering as well as for individuals preparing for a career in mathematics education.
Non Associative Linear Algebras
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Author : W. B. Vasantha Kandasamy, Florentin Smarandache
language : en
Publisher: Infinite Study
Release Date : 2012
Non Associative Linear Algebras written by W. B. Vasantha Kandasamy, Florentin Smarandache and has been published by Infinite Study this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012 with Mathematics categories.
Lectures In General Algebra
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Author : A. G. Kurosh
language : en
Publisher: Elsevier
Release Date : 2014-07-10
Lectures In General Algebra written by A. G. Kurosh and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-07-10 with Mathematics categories.
Lectures in General Algebra is a translation from the Russian and is based on lectures on specialized courses in general algebra at Moscow University. The book starts with the basics of algebra. The text briefly describes the theory of sets, binary relations, equivalence relations, partial ordering, minimum condition, and theorems equivalent to the axiom of choice. The text gives the definition of binary algebraic operation and the concepts of groups, groupoids, and semigroups. The book examines the parallelism between the theory of groups and the theory of rings; such examinations show the convenience of constructing a single theory from the results of group experiments and ring experiments which are known to follow simple corollaries. The text also presents algebraic structures that are not of binary nature. From this parallelism arise other concepts, such as that of the lattices, complete lattices, and modular lattices. The book then proves the Schmidt-Ore theorem, and also describes linear algebra, as well as the Birkhoff-Witt theorem on Lie algebras. The text also addresses ordered groups, the Archimedean groups and rings, and Albert's theorem on normed algebras. This book can prove useful for algebra students and for professors of algebra and advanced mathematicians.
An Introduction To Nonassociative Algebras
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Author :
language : en
Publisher: Academic Press
Release Date : 2011-08-29
An Introduction To Nonassociative Algebras written by and has been published by Academic Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-08-29 with Mathematics categories.
An Introduction to Nonassociative Algebras