Algebraic Structures Using Subsets
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Algebraic Structures Using Subsets
Author | : W. B. Vasantha Kandasamy, Florentin Smarandache |
Publsiher | : Infinite Study |
Total Pages | : 199 |
Release | : 2012 |
Genre | : Algebra, Boolean |
ISBN | : 9781599732169 |
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"[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."--
An Introduction to Algebraic Structures
Author | : Joseph Landin |
Publsiher | : Courier Corporation |
Total Pages | : 275 |
Release | : 2012-08-29 |
Genre | : Mathematics |
ISBN | : 9780486150413 |
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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.
Subset Polynomial Semirings and Subset Matrix Semirings
Author | : W. B. Vasantha Kandasamy,Florentin Smarandache |
Publsiher | : Infinite Study |
Total Pages | : 269 |
Release | : 2013 |
Genre | : Mathematics |
ISBN | : 9781599732237 |
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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.
Algebraic Structures on MOD Planes
Author | : W. B. Vasantha Kandasamy,K. Ilanthenral,Florentin Smarandache |
Publsiher | : Infinite Study |
Total Pages | : 215 |
Release | : 2015-11-01 |
Genre | : Algebras, Linear |
ISBN | : 9781599733678 |
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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.
Subset Groupoids
Author | : W. B. Vasantha Kandasamy, Florentin Smarandache |
Publsiher | : Infinite Study |
Total Pages | : 151 |
Release | : 2013 |
Genre | : Mathematics |
ISBN | : 9781599732220 |
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MOD Natural Neutrosophic Subset Semigroups
Author | : W. B. Vasantha Kandasamy ,Ilanthenral K,Florentin Smarandache |
Publsiher | : Infinite Study |
Total Pages | : 135 |
Release | : 2024 |
Genre | : Electronic Book |
ISBN | : 9781599734859 |
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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
MOD Natural Neutrosophic Subset Topological Spaces and Kakutani s Theorem
Author | : W. B. Vasantha Kandasamy,K. Ilanthenral,Florentin Smarandche |
Publsiher | : Infinite Study |
Total Pages | : 135 |
Release | : 2024 |
Genre | : Electronic Book |
ISBN | : 9781599734903 |
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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.
Smarandache Special Definite Algebraic Structures
Author | : W. B. Vasantha Kandasamy |
Publsiher | : Infinite Study |
Total Pages | : 141 |
Release | : 2009-01-01 |
Genre | : Mathematics |
ISBN | : 9781599730851 |
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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.