Author: W. B. Vasantha Kandasamy, Florentin Smarandache
Publisher: Infinite Study
ISBN: 1599732165
Category : Algebra, Boolean
Languages : en
Pages : 199
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Book Description
"[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
ISBN: 0486150410
Category : Mathematics
Languages : en
Pages : 275
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Book Description
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
Publisher: Infinite Study
ISBN: 1599732238
Category : Mathematics
Languages : en
Pages : 269
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Book Description
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
Publisher: Infinite Study
ISBN: 1599733676
Category : Algebras, Linear
Languages : en
Pages : 215
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Book Description
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
Publisher: Infinite Study
ISBN: 1599730855
Category : Mathematics
Languages : en
Pages : 141
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Book Description
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, Florentin Smarandache
Publisher: Infinite Study
ISBN: 159973222X
Category : Mathematics
Languages : en
Pages : 151
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Book Description
Author: W. B. Vasantha Kandasamy
Publisher: Infinite Study
ISBN: 1599734850
Category :
Languages : en
Pages :
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Book Description
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
ISBN: 1599734907
Category :
Languages : en
Pages :
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Book Description
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
Publisher: Infinite Study
ISBN: 1599733684
Category : Algebras, Linear
Languages : en
Pages : 209
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Book Description
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
ISBN: 9811220336
Category : Mathematics
Languages : en
Pages : 393
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Book Description
'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.
