Algebras And Smarandache Types

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Linear Algebra and Smarandache Linear Algebra

Author : W. B. Vasantha Kandasamy
Publisher : Infinite Study
ISBN 13 : 1931233756
Total Pages : 175 pages
Book Rating : 4.9/5 (312 download)

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Book Synopsis Linear Algebra and Smarandache Linear Algebra by : W. B. Vasantha Kandasamy

Download or read book Linear Algebra and Smarandache Linear Algebra written by W. B. Vasantha Kandasamy and published by Infinite Study. This book was released on 2003 with total page 175 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this book the author analyzes the Smarandache linear algebra, and introduces several other concepts like the Smarandache semilinear algebra, Smarandache bilinear algebra and Smarandache anti-linear algebra. We indicate that Smarandache vector spaces of type II will be used in the study of neutrosophic logic and its applications to Markov chains and Leontief Economic models ? both of these research topics have intense industrial applications. The Smarandache linear algebra, is defined to be a Smarandache vector space of type II, on which there is an additional operation called product, such that for all a, b in V, ab is in V.The Smarandache vector space of type II is defined to be a module V defined over a Smarandache ring R such that V is a vector space over a proper subset k of R, where k is a field.

Algebras and Smarandache Types

Author : Hee Sik Kim
Publisher : Infinite Study
ISBN 13 :
Total Pages : 6 pages
Book Rating : 4./5 ( download)

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Book Synopsis Algebras and Smarandache Types by : Hee Sik Kim

Download or read book Algebras and Smarandache Types written by Hee Sik Kim and published by Infinite Study. This book was released on with total page 6 pages. Available in PDF, EPUB and Kindle. Book excerpt: If an algebra of type A contains a subalgebra which is also an algebra of type B, then it is a Smarandache B-type A-algebra provided the subalgebra of type B contains at least two elements. This generalizes the notion of Smarandache group, where the group of order 2 is a subsemigroup of a semigroup. In this paper we investigate a number of such pairings and we deduce a number of conclusions as a consequence.

Smarandache Fuzzy Algebra

Author : W. B. Vasantha Kandasamy
Publisher : Infinite Study
ISBN 13 : 1931233748
Total Pages : 455 pages
Book Rating : 4.9/5 (312 download)

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Book Synopsis Smarandache Fuzzy Algebra by : W. B. Vasantha Kandasamy

Download or read book Smarandache Fuzzy Algebra written by W. B. Vasantha Kandasamy and published by Infinite Study. This book was released on 2003 with total page 455 pages. Available in PDF, EPUB and Kindle. Book excerpt: The author studies the Smarandache Fuzzy Algebra, which, like its predecessor Fuzzy Algebra, arose from the need to define structures that were more compatible with the real world where the grey areas mattered, not only black or white.In any human field, a Smarandache n-structure on a set S means a weak structure {w(0)} on S such that there exists a chain of proper subsets P(n-1) in P(n-2) in?in P(2) in P(1) in S whose corresponding structures verify the chain {w(n-1)} includes {w(n-2)} includes? includes {w(2)} includes {w(1)} includes {w(0)}, where 'includes' signifies 'strictly stronger' (i.e., structure satisfying more axioms).This book is referring to a Smarandache 2-algebraic structure (two levels only of structures in algebra) on a set S, i.e. a weak structure {w(0)} on S such that there exists a proper subset P of S, which is embedded with a stronger structure {w(1)}. Properties of Smarandache fuzzy semigroups, groupoids, loops, bigroupoids, biloops, non-associative rings, birings, vector spaces, semirings, semivector spaces, non-associative semirings, bisemirings, near-rings, non-associative near-ring, and binear-rings are presented in the second part of this book together with examples, solved and unsolved problems, and theorems. Also, applications of Smarandache groupoids, near-rings, and semirings in automaton theory, in error correcting codes, and in the construction of S-sub-biautomaton can be found in the last chapter.

Smarandache Non-Associative Rings

Author : W. B. Vasantha Kandasamy
Publisher : Infinite Study
ISBN 13 : 1931233691
Total Pages : 151 pages
Book Rating : 4.9/5 (312 download)

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Book Synopsis Smarandache Non-Associative Rings by : W. B. Vasantha Kandasamy

Download or read book Smarandache Non-Associative Rings written by W. B. Vasantha Kandasamy and published by Infinite Study. This book was released on 2002 with total page 151 pages. Available in PDF, EPUB and Kindle. Book excerpt: Generally, in any human field, a Smarandache Structure on a set A means a weak structure W on A such that there exists a proper subset B in A which is embedded with a stronger structure S. These types of structures occur in our everyday's life, that's why we study them in this book. Thus, as a particular case: A Non-associative ring is a non-empty set R together with two binary operations '+' and '.' such that (R, +) is an additive abelian group and (R, .) is a groupoid. For all a, b, c in R we have (a + b) . c = a . c + b . c and c . (a + b) = c . a + c . b. A Smarandache non-associative ring is a non-associative ring (R, +, .) which has a proper subset P in R, that is an associative ring (with respect to the same binary operations on R).

Generalized Fibonacci sequences in groupoids

Author : Hee Sik Kim
Publisher : Infinite Study
ISBN 13 :
Total Pages : 10 pages
Book Rating : 4./5 ( download)

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Book Synopsis Generalized Fibonacci sequences in groupoids by : Hee Sik Kim

Download or read book Generalized Fibonacci sequences in groupoids written by Hee Sik Kim and published by Infinite Study. This book was released on with total page 10 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this paper, we introduce the notion of generalized Fibonacci sequences over a groupoid and discuss it in particular for the case where the groupoid contains idempotents and pre-idempotents. Using the notion of Smarandache-type P-algebra, we obtain several relations on groupoids which are derived from generalized Fibonacci sequences.

Interval Linear Algebra

Author : W. B. Vasantha Kandasamy, Florentin Smarandache
Publisher : Infinite Study
ISBN 13 : 1599731266
Total Pages : 249 pages
Book Rating : 4.5/5 (997 download)

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Book Synopsis Interval Linear Algebra by : W. B. Vasantha Kandasamy, Florentin Smarandache

Download or read book Interval Linear Algebra written by W. B. Vasantha Kandasamy, Florentin Smarandache and published by Infinite Study. This book was released on 2010 with total page 249 pages. Available in PDF, EPUB and Kindle. Book excerpt: Interval Arithmetic, or Interval Mathematics, was developed in the 1950s and 1960s as an approach to rounding errors in mathematical computations. However, there was no methodical development of interval algebraic structures to this date.This book provides a systematic analysis of interval algebraic structures, viz. interval linear algebra, using intervals of the form [0, a].

On the structure of general algebras and its applications

Author : Young Joo Seo
Publisher : Infinite Study
ISBN 13 :
Total Pages : 79 pages
Book Rating : 4./5 ( download)

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Book Synopsis On the structure of general algebras and its applications by : Young Joo Seo

Download or read book On the structure of general algebras and its applications written by Young Joo Seo and published by Infinite Study. This book was released on with total page 79 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this thesis, we discuss some structural theory of a d-algebra which is a generalization of a BCK-algebra, and wedis uss analytic real algebras. We investigate several conditions for analytic real algebras to be d-algebras. Moreover, we introduce the notion of a Smarandacheness to BCI-algebras, and obtain several properties on Smarandache fuzzy BCI-algebras.

Advancements in Science and Technology for Healthcare, Agriculture, and Environmental Sustainability

Author : Dimitrios A Karras
Publisher : CRC Press
ISBN 13 : 1040001750
Total Pages : 692 pages
Book Rating : 4.0/5 (4 download)

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Book Synopsis Advancements in Science and Technology for Healthcare, Agriculture, and Environmental Sustainability by : Dimitrios A Karras

Download or read book Advancements in Science and Technology for Healthcare, Agriculture, and Environmental Sustainability written by Dimitrios A Karras and published by CRC Press. This book was released on 2024-06-13 with total page 692 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is the collection of selected articles that appeared at the First International Analytics Conference 2023 held in Hyderabad in virtual mode on February 2nd the 3rd 2023. This informative volume offers a window into recent breakthroughs shaping healthcare, agriculture, and environmental sustainability. It showcases the cutting-edge developments in these essential fields. Explore the progress in healthcare, from personalized medicine to telemedicine and innovative treatments, demonstrating how technology is enhancing patient care and transforming global health. Dive into the agricultural sector, where precision farming, genetic engineering, and sustainable practices are revolutionizing food production. Science and innovation play a key role in building a more resilient and food-secure future.

A note on UP-hyperalgebras

Author : A. Iampan
Publisher : Infinite Study
ISBN 13 :
Total Pages : 19 pages
Book Rating : 4./5 ( download)

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Book Synopsis A note on UP-hyperalgebras by : A. Iampan

Download or read book A note on UP-hyperalgebras written by A. Iampan and published by Infinite Study. This book was released on with total page 19 pages. Available in PDF, EPUB and Kindle. Book excerpt: We introduce the concept of UP-hyperalgebras which is a generalization of UP-algebras, and investigate some related properties.

NEUTROSOPHIC TRIPLET STRUCTURES, Volume I

Author : Florentin Smarandache
Publisher : Infinite Study
ISBN 13 :
Total Pages : 21 pages
Book Rating : 4./5 ( download)

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Book Synopsis NEUTROSOPHIC TRIPLET STRUCTURES, Volume I by : Florentin Smarandache

Download or read book NEUTROSOPHIC TRIPLET STRUCTURES, Volume I written by Florentin Smarandache and published by Infinite Study. This book was released on with total page 21 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this chapter, we introduce neutrosophic triplet cosets for neutrosophic triplet G-module and neutrosophic triplet quotient G-module. Then, we give some definitions and examples for neutrosophic triplet quotient G-module and neutrosophic triplet cosets. Also, we obtain isomorphism theorems for neutrosophic triplet G-modules and we prove isomorphism theorems for neutrosophic triplet G-modules.

Neutrosophic subalgebras of several types in BCK/BCI-algebras

Author : Young Bae Jun
Publisher : Infinite Study
ISBN 13 :
Total Pages : 12 pages
Book Rating : 4./5 ( download)

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Book Synopsis Neutrosophic subalgebras of several types in BCK/BCI-algebras by : Young Bae Jun

Download or read book Neutrosophic subalgebras of several types in BCK/BCI-algebras written by Young Bae Jun and published by Infinite Study. This book was released on with total page 12 pages. Available in PDF, EPUB and Kindle. Book excerpt: Conditions for a neutrosophic set to be a (q, ∈∨q)-neutrosophic subalgebra are considered.

Smarandache Semigroups

Author : W. B. Vasantha Kandasamy
Publisher : Infinite Study
ISBN 13 : 1931233594
Total Pages : 95 pages
Book Rating : 4.9/5 (312 download)

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Book Synopsis Smarandache Semigroups by : W. B. Vasantha Kandasamy

Download or read book Smarandache Semigroups written by W. B. Vasantha Kandasamy and published by Infinite Study. This book was released on 2002-12-01 with total page 95 pages. Available in PDF, EPUB and Kindle. Book excerpt: Generally, in any human field, a Smarandache Structure on a set A means a weak structure W on A such that there exists a proper subset B in A which is embedded with a stronger structure S.These types of structures occur in our everyday life, that?s why we study them in this book.Thus, as a particular case:A Smarandache Semigroup is a semigroup A which has a proper subset B in A that is a group (with respect to the same binary operation on A).

Scientiae Mathematicae Japonicae

Author :
Publisher :
ISBN 13 :
Total Pages : 652 pages
Book Rating : 4.E/5 ( download)

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Book Synopsis Scientiae Mathematicae Japonicae by :

Download or read book Scientiae Mathematicae Japonicae written by and published by . This book was released on 2001 with total page 652 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Dual Numbers

Author : W. B. Vasantha Kandasamy, Florentin Smarandache
Publisher : Infinite Study
ISBN 13 : 1599731843
Total Pages : 161 pages
Book Rating : 4.5/5 (997 download)

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Book Synopsis Dual Numbers by : W. B. Vasantha Kandasamy, Florentin Smarandache

Download or read book Dual Numbers written by W. B. Vasantha Kandasamy, Florentin Smarandache and published by Infinite Study. This book was released on with total page 161 pages. Available in PDF, EPUB and Kindle. Book excerpt:

New Trends in Neutrosophic Theory and Applications

Author : Florentin Smarandache (editor)
Publisher : Infinite Study
ISBN 13 : 1599734982
Total Pages : 426 pages
Book Rating : 4.5/5 (997 download)

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Book Synopsis New Trends in Neutrosophic Theory and Applications by : Florentin Smarandache (editor)

Download or read book New Trends in Neutrosophic Theory and Applications written by Florentin Smarandache (editor) and published by Infinite Study. This book was released on 2016-11-05 with total page 426 pages. Available in PDF, EPUB and Kindle. Book excerpt: Neutrosophic theory and applications have been expanding in all directions at an astonishing rate especially after the introduction the journal entitled “Neutrosophic Sets and Systems”. New theories, techniques, algorithms have been rapidly developed. One of the most striking trends in the neutrosophic theory is the hybridization of neutrosophic set with other potential sets such as rough set, bipolar set, soft set, hesitant fuzzy set, etc. The different hybrid structure such as rough neutrosophic set, single valued neutrosophic rough set, bipolar neutrosophic set, single valued neutrosophic hesitant fuzzy set, etc. are proposed in the literature in a short period of time. Neutrosophic set has been a very important tool in all various areas of data mining, decision making, e-learning, engineering, medicine, social science, and some more. The book “New Trends in Neutrosophic Theories and Applications” focuses on theories, methods, algorithms for decision making and also applications involving neutrosophic information. Some topics deal with data mining, decision making, e-learning, graph theory, medical diagnosis, probability theory, topology, and some more. 30 papers by 39 authors and coauthors.

MBJ-neutrosophic filters of equality algebras

Author : M. Mohseni Takallo
Publisher : Infinite Study
ISBN 13 :
Total Pages : 19 pages
Book Rating : 4./5 ( download)

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Book Synopsis MBJ-neutrosophic filters of equality algebras by : M. Mohseni Takallo

Download or read book MBJ-neutrosophic filters of equality algebras written by M. Mohseni Takallo and published by Infinite Study. This book was released on with total page 19 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this paper, we introduce the notion of MBJneutrosophic sub-algebra and MBJ-neutrosophic lter on equality algebras and investigate some equivalence de finitions, properties and the relation between them. Also, by using the notion of MBJ-neutrosophic lter, we introduce a congruence relation on equality algebra and show that the quotient is an equality algebra.

n-Linear Algebra of Type 1 and Its Applications

Author : W. B. Vasantha Kandasamy
Publisher : Infinite Study
ISBN 13 : 159973074X
Total Pages : 122 pages
Book Rating : 4.5/5 (997 download)

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Book Synopsis n-Linear Algebra of Type 1 and Its Applications by : W. B. Vasantha Kandasamy

Download or read book n-Linear Algebra of Type 1 and Its Applications written by W. B. Vasantha Kandasamy and published by Infinite Study. This book was released on 2008 with total page 122 pages. Available in PDF, EPUB and Kindle. Book excerpt: n-Linear Algebra of type I introduced in this book find applications in Markov chains and Leontief economic models.Innovative scientists and engineers can adopt this concept in Fuzzy Finite Element analysis of mechanical structures with uncertain parameters.