Algebraic Structures Using Subsets

Author : W. B. Vasantha Kandasamy, Florentin Smarandache
Publisher : Infinite Study
Page : 199 pages
File Size : 43,9 Mb
Release : 2012
Category : Algebra, Boolean
ISBN : 9781599732169

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Algebraic Structures Using Subsets by W. B. Vasantha Kandasamy, Florentin Smarandache Pdf

"[The] study of algebraic structures using subsets [was] started by George Boole. After the invention of Boolean algebra, subsets are not used in building any algebraic structures. In this book we develop algebraic structures using subsets of a set or a group, or a semiring, or a ring, and get algebraic structures. Using group or semigroup, we only get subset semigroups. Using ring or semiring, we get only subset semirings. By this method, we get [an] infinite number of non-commutative semirings of finite order. We build subset semivector spaces, [and] describe and develop several interesting properties about them."--

Author : Joseph Landin
Publisher : Courier Corporation
Page : 275 pages
File Size : 53,9 Mb
Release : 2012-08-29
Category : Mathematics
ISBN : 9780486150413

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An Introduction to Algebraic Structures by Joseph Landin Pdf

This self-contained text covers sets and numbers, elements of set theory, real numbers, the theory of groups, group isomorphism and homomorphism, theory of rings, and polynomial rings. 1969 edition.

Author : W. B. Vasantha Kandasamy,Florentin Smarandache
Publisher : Infinite Study
Page : 269 pages
File Size : 48,6 Mb
Release : 2013
Category : Mathematics
ISBN : 9781599732237

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Subset Polynomial Semirings and Subset Matrix Semirings by W. B. Vasantha Kandasamy,Florentin Smarandache Pdf

In this book the authors introduce the new notions of subset polynomial semirings and subset matrix semirings. Solving subset polynomial equations is an interesting exercise. Open problems about the solution set of subset polynomials are proposed.

Author : W. B. Vasantha Kandasamy,K. Ilanthenral,Florentin Smarandache
Publisher : Infinite Study
Page : 215 pages
File Size : 46,7 Mb
Release : 2015-11-01
Category : Algebras, Linear
ISBN : 9781599733678

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Algebraic Structures on MOD Planes by W. B. Vasantha Kandasamy,K. Ilanthenral,Florentin Smarandache Pdf

Study of MOD planes happens to a very recent one. In this book, systematically algebraic structures on MOD planes like, MOD semigroups, MOD groups and MOD rings of different types are defined and studied. Such study is innovative for a large four quadrant planes are made into a small MOD planes. Several distinct features enjoyed by these MOD planes are defined, developed and described.

Author : W. B. Vasantha Kandasamy, Florentin Smarandache
Publisher : Infinite Study
Page : 151 pages
File Size : 45,9 Mb
Release : 2013
Category : Mathematics
ISBN : 9781599732220

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Subset Groupoids by W. B. Vasantha Kandasamy, Florentin Smarandache Pdf

Author : W. B. Vasantha Kandasamy ,Ilanthenral K,Florentin Smarandache
Publisher : Infinite Study
Page : 128 pages
File Size : 54,5 Mb
Release : 2024-05-20
Category : Electronic
ISBN : 9781599734859

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MOD Natural Neutrosophic Subset Semigroups by W. B. Vasantha Kandasamy ,Ilanthenral K,Florentin Smarandache Pdf

In this book the authors introduce for the first time the MOD Natural Subset Semigroups. They enjoy very many special properties. They are only semigroups even under addition. This book provides several open problems to the semigroup theorists

Author : W. B. Vasantha Kandasamy
Publisher : Infinite Study
Page : 141 pages
File Size : 55,6 Mb
Release : 2009-01-01
Category : Mathematics
ISBN : 9781599730851

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Smarandache Special Definite Algebraic Structures by W. B. Vasantha Kandasamy Pdf

We study these new Smarandache algebraic structures, which are defined as structures which have a proper subset which has a weak structure.A Smarandache Weak Structure on a set S means a structure on S that has a proper subset P with a weaker structure.By proper subset of a set S, we mean a subset P of S, different from the empty set, from the original set S, and from the idempotent elements if any.A Smarandache Strong Structure on a set S means a structure on S that has a proper subset P with a stronger structure.A Smarandache Strong-Weak Structure on a set S means a structure on S that has two proper subsets: P with a stronger structure, and Q with a weaker structure.

Author : W. B. Vasantha Kandasamy,K. Ilanthenral,Florentin Smarandche
Publisher : Infinite Study
Page : 128 pages
File Size : 40,7 Mb
Release : 2024-05-20
Category : Electronic
ISBN : 9781599734903

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MOD Natural Neutrosophic Subset Topological Spaces and Kakutani’s Theorem by W. B. Vasantha Kandasamy,K. Ilanthenral,Florentin Smarandche Pdf

In this book authors for the first time develop the notion of MOD natural neutrosophic subset special type of topological spaces using MOD natural neutrosophic dual numbers or MOD natural neutrosophic finite complex number or MOD natural neutrosophic-neutrosophic numbers and so on to build their respective MOD semigroups. Later they extend this concept to MOD interval subset semigroups and MOD interval neutrosophic subset semigroups. Using these MOD interval semigroups and MOD interval natural neutrosophic subset semigroups special type of subset topological spaces are built. Further using these MOD subsets we build MOD interval subset matrix semigroups and MOD interval subset matrix special type of matrix topological spaces. Likewise using MOD interval natural neutrosophic subsets matrices semigroups we can build MOD interval natural neutrosophic matrix subset special type of topological spaces. We also do build MOD subset coefficient polynomial special type of topological spaces. The final chapter mainly proposes several open conjectures about the validity of the Kakutani’s fixed point theorem for all MOD special type of subset topological spaces.

Author : W. B. Vasantha Kandasamy,K. Ilanthenral,Florentin Smarandache
Publisher : Infinite Study
Page : 209 pages
File Size : 47,6 Mb
Release : 2015
Category : Algebras, Linear
ISBN : 9781599733685

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Non-Associative Algebraic Structures on MOD Planes by W. B. Vasantha Kandasamy,K. Ilanthenral,Florentin Smarandache Pdf

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.

Author : Marco Grandis
Publisher : World Scientific
Page : 393 pages
File Size : 41,9 Mb
Release : 2020-08-12
Category : Mathematics
ISBN : 9789811220333

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Elementary Overview Of Mathematical Structures, An: Algebra, Topology And Categories by Marco Grandis Pdf

'The presentation is modeled on the discursive style of the Bourbaki collective, and the coverage of topics is rich and varied. Grandis has provided a large selection of exercises and has sprinkled orienting comments throughout. For an undergraduate library where strong students seek an overview of a significant portion of mathematics, this would be an excellent acquisition. Summing up: Recommended.'CHOICESince the last century, a large part of Mathematics is concerned with the study of mathematical structures, from groups to fields and vector spaces, from lattices to Boolean algebras, from metric spaces to topological spaces, from topological groups to Banach spaces.More recently, these structured sets and their transformations have been assembled in higher structures, called categories.We want to give a structural overview of these topics, where the basic facts of the different theories are unified through the 'universal properties' that they satisfy, and their particularities stand out, perhaps even more.This book can be used as a textbook for undergraduate studies and for self-study. It can provide students of Mathematics with a unified perspective of subjects which are often kept apart. It is also addressed to students and researchers of disciplines having strong interactions with Mathematics, like Physics and Chemistry, Statistics, Computer Science, Engineering.

Author : Palash B. Pal
Publisher : Cambridge University Press
Page : 717 pages
File Size : 40,6 Mb
Release : 2019-05-23
Category : Science
ISBN : 9781108492201

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A Physicists Introduction to Algebraic Structures by Palash B. Pal Pdf

Algebraic structures including vector space, groups, topological spaces and more, all covered in one volume, showing the mutual connections.

Author : W. B. Vasantha Kandasamy,Florentin Smarandache
Publisher : Infinite Study
Page : 209 pages
File Size : 40,9 Mb
Release : 2024-05-20
Category : Electronic
ISBN : 9781599732251

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Subset Non Associative Semirings by W. B. Vasantha Kandasamy,Florentin Smarandache Pdf

Author : Jorge Martínez,W.C. Holland
Publisher : Springer Science & Business Media
Page : 257 pages
File Size : 54,5 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9789401117234

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Ordered Algebraic Structures by Jorge Martínez,W.C. Holland Pdf

This volume contains a selection of papers presented at the 1991 Conrad Conference, held in Gainesville, Florida, USA, in December, 1991. Together, these give an overview of some recent advances in the area of ordered algebraic structures. The first part of the book is devoted to ordered permutation groups and universal, as well as model-theoretic, aspects. The second part deals with material variously connected to general topology and functional analysis. Collectively, the contents of the book demonstrate the wide applicability of order-theoretic methods, and how ordered algebraic structures have connections with many research disciplines. For researchers and graduate students whose work involves ordered algebraic structures.

Author : George R. Kempf
Publisher : Springer Science & Business Media
Page : 174 pages
File Size : 45,9 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783322802781

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Algebraic Structures by George R. Kempf Pdf

In algebra there are four basic structures: groups, rings, fields and modules. In this book the theory of these basic structures is presented and the laws of composition - the basic operations of algebra - are studied. Essentially, no previous knowledge is required, it is only assumed as background that the reader has learned some linear algebra over the real numbers.Dieses Lehrbuch, verfasst von einem anerkannten amerikanischen Mathematiker, ist eine unkonventionelle Einführung in die Algebra. Es gibt vier grundlegende Strukturen in der Algebra: Gruppen, Ringe, Körper und Moduln. Das Buch behandelt die Theorie dieser Strukturen und beschreibt die Verknüpfungsregeln, die grundlegenden Operationen der Algebra. Die Darstellung ist elementar: es werden nur Kenntnisse der Linearen Algebra vorausgesetzt, weitere Fachkenntnisse sind nicht erforderlich.

Author : Sanjay Moreshwar Wagh
Publisher : Taylor & Francis
Page : 440 pages
File Size : 40,6 Mb
Release : 2017-12-22
Category : Science
ISBN : 9781351238311

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Subtlety in Relativity by Sanjay Moreshwar Wagh Pdf

Subtlety in Relativity is the only book that has been written after the author’s discovery of a new way in which wave phenomena occur—the emission origin of waves. This drastically changes most issues of the old debate over the world being either deterministic or probabilistic. The emission origin of waves is not incompatible with the ideas of quantum theory; rather, this new and novel way in which waves can be generated justifies the use of mathematical and probabilistic methods of quantum theory. However, the emission origin of waves shows that quantum theory is statistically incomplete in, precisely, Einstein’s sense. There exists, then, a certain, previously unexplored, conceptual framework underlying the ideas of quantum theory. Whether this is the theory that Einstein and others were looking for then, how this way of thinking is related to the ideas of relativity, and whether this is a relativistic theory in the usual sense of this word are questions this book answers. The book demonstrates how the Doppler effect with acceleration is essential to interpreting astronomical observations. It also offers a detailed and self-sufficient technical background of mathematical ideas of category theory. The book is divided into two parts. The first is less mathematical and more conceptual in its orientation. The second focuses on mathematical ideas needed to implement physical concepts. The book is a great reference for advanced undergraduate- and graduate-level students of physics and researchers in physics, astronomy, and cosmology, who will gain a deeper understanding of relativity from it.