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Algebras And Smarandache Types
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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 2018-01-01 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 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.
Book Synopsis Smarandache BE-Algebras by : Arsham Borumand Saeid
Download or read book Smarandache BE-Algebras written by Arsham Borumand Saeid and published by Infinite Study. This book was released on with total page 65 pages. Available in PDF, EPUB and Kindle. Book excerpt: v\:* {behavior:url(#default#VML);} o\:* {behavior:url(#default#VML);} w\:* {behavior:url(#default#VML);} .shape {behavior:url(#default#VML);} Normal 0 false false false EN-US X-NONE X-NONE /* Style Definitions */ table.MsoNormalTable {mso-style-name:"Table Normal"; mso-tstyle-rowband-size:0; mso-tstyle-colband-size:0; mso-style-noshow:yes; mso-style-priority:99; mso-style-parent:""; mso-padding-alt:0in 5.4pt 0in 5.4pt; mso-para-margin-top:0in; mso-para-margin-right:0in; mso-para-margin-bottom:8.0pt; mso-para-margin-left:0in; line-height:107%; mso-pagination:widow-orphan; font-size:11.0pt; font-family:"Calibri","sans-serif"; mso-ascii-font-family:Calibri; mso-ascii-theme-font:minor-latin; mso-hansi-font-family:Calibri; mso-hansi-theme-font:minor-latin;} There are three types of Smarandache Algebraic Structures: 1. 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 Weak Structure on a set S means a structure on S that has a proper subset P with a weaker 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. By proper subset of a set S, one understands a subset P of S, different from the empty set, from the original set S, and from the idempotent elements if any. Having two structures {u} and {v} defined by the same operations, one says that structure {u} is stronger than structure {v}, i.e. {u} > {v}, if the operations of {u} satisfy more axioms than the operations of {v}. Each one of the first two structure types is then generalized from a 2-level (the sets P ⊂ S and their corresponding strong structure {w1}>{w0}, respectively their weak structure {w1}<{w0}) to an n-level (the sets Pn-1 ⊂ Pn-2 ⊂ … ⊂ P2 ⊂ P1 ⊂ S and their corresponding strong structure {wn-1} > {wn-2} > … > {w2} > {w1} > {w0}, or respectively their weak structure {wn-1} < {wn-2} < … < {w2} < {w1} < {w0}). Similarly for the third structure type, whose generalization is a combination of the previous two structures at the n-level. A Smarandache Weak BE-Algebra X is a BE-algebra in which there exists a proper subset Q such that 1 Q, |Q| ≥ 2, and Q is a CI-algebra. And a Smarandache Strong CI-Algebra X is a CI-algebra X in which there exists a proper subset Q such that 1 Q, |Q| ≥ 2, and Q is a BE-algebra. The book elaborates a recollection of the BE/CI-algebras, then introduces these last two particular structures and studies their properties.
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.
Book Synopsis Smarandache N{subalgebras(resp. lters) of CI-algebras by : Akbar Rezaei
Download or read book Smarandache N{subalgebras(resp. lters) of CI-algebras written by Akbar Rezaei and published by Infinite Study. This book was released on with total page 12 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this paper, we introduce the notions of N-subalgebras and N- lters based on Smarandache CI-algebra and give a number of their properties. The relationship between N(Q; f)-subalgebras( lters) and N-subalgebras( lters) are also investigated.
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.
Book Synopsis Smarandache N-subalgebras(resp. filters) of CI-algebras by : Akbar Rezaei
Download or read book Smarandache N-subalgebras(resp. filters) of CI-algebras written by Akbar Rezaei and published by Infinite Study. This book was released on with total page 12 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this paper, we introduce the notions of N-subalgebras and N- lters based on Smarandache CI-algebra andgive a number of their properties. The relationship between N(Q; f)-subalgebras( lters) and N-subalgebras( lters) are also investigated.
Book Synopsis Q-Smarandache Fuzzy Implicative Ideal of QSmarandache BH-Algebra by : Husein Hadi Abbass
Download or read book Q-Smarandache Fuzzy Implicative Ideal of QSmarandache BH-Algebra written by Husein Hadi Abbass and published by Infinite Study. This book was released on with total page 15 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this paper, The notions of Q-Smarandache fuzzy implicative ideal and Q- Smarandache fuzzy sub implicative ideal of a Q-Smarandache BH-Algebra introduced, examples are given, and related properties investigated the relationships among these notions and other types of Q-Smarandache fuzzy ideal of a Q-Smarandache BH-Algebra are studied.
Book Synopsis Smarandache N-subalgebras (resp. filters) of CI-algebras by : Akbar Rezaei
Download or read book Smarandache N-subalgebras (resp. filters) of CI-algebras written by Akbar Rezaei and published by Infinite Study. This book was released on with total page 12 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this paper, we introduce the notions of N-subalgebras and N-filters based on Smarandache CI-algebra and give a number of their properties.
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.
Author :W. B. Vasantha Kandasamy, Florentin Smarandache Publisher :Infinite Study ISBN 13 :1599732165 Total Pages :199 pages Book Rating :4.5/5 (997 download)
Book Synopsis Algebraic Structures Using Subsets by : W. B. Vasantha Kandasamy, Florentin Smarandache
Download or read book Algebraic Structures Using Subsets written by W. B. Vasantha Kandasamy, Florentin Smarandache and published by Infinite Study. This book was released on 2012 with total page 199 pages. Available in PDF, EPUB and Kindle. Book excerpt: "[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."--
Book Synopsis On a Q- Smarandache Implicative Ideal with Respect to an Element of a Q-Smarandache BH-algebra by : Husein Hadi Abbass
Download or read book On a Q- Smarandache Implicative Ideal with Respect to an Element of a Q-Smarandache BH-algebra written by Husein Hadi Abbass and published by Infinite Study. This book was released on with total page 9 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this paper, we define the concept of a Q-Smarandache implicative ideal with respect to an element of a Q-Smarandache BH-algebra. We state and prove some theorems which determine the relationships among this notion and other types of ideals of a Q-Smarandache BH-algebra.
Book Synopsis On a Q-Smarandache Fuzzy Commutative Ideal of a Q-Smarandache BH-algebra by : Husein Hadi Abbass
Download or read book On a Q-Smarandache Fuzzy Commutative Ideal of a Q-Smarandache BH-algebra written by Husein Hadi Abbass and published by Infinite Study. This book was released on with total page 11 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this paper, the notions of Q-Smarandache fuzzy commutative ideal and Q-Smarandache fuzzy sub-commutative ideal of a Q-Smarandache BH-Algebra are introduced, examples and related properties are investigated. Also, the relationships among these notions and other types of Q-Smarandache fuzzy ideal of a Q-Smarandache BH-Algebra are studied.
Book Synopsis Smarandache Fresh and Clean Ideals of Smarandache BCI- algebras by : Young Bae Jun
Download or read book Smarandache Fresh and Clean Ideals of Smarandache BCI- algebras written by Young Bae Jun and published by Infinite Study. This book was released on with total page 9 pages. Available in PDF, EPUB and Kindle. Book excerpt: The notion of Smarandache fresh and clean ideals is introduced, examples are given, and related properties are investigated. Relations between Q-Smarandache fresh ideals and Q-Smarandache clean ideals are given. Extension properties for Q-Smarandache fresh ideals and Q-Smarandache clean ideals are established.
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).
Book Synopsis On a Psеuԁo Smarandache Idea ls of BH algebra by : Husein Hadi Abbass
Download or read book On a Psеuԁo Smarandache Idea ls of BH algebra written by Husein Hadi Abbass and published by Infinite Study. This book was released on with total page 4 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this paper the notion of a pseudo Samarandache BH-algebra, a psҽuԁo Samarandache ideal, a psҽudo Smarandache closed ideal and a psҽudo Samarandache completely closed ideal of a pseudo Samarandache BH-algebra are defined. There notion are stadied. The relationships among these types of ideals are discussed.
Author :W. B. Vasantha Kandasamy, Florentin Smarandache Publisher :Infinite Study ISBN 13 :1599731266 Total Pages :249 pages Book Rating :4.5/5 (997 download)
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].
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 Bookman Publishing & Marketing. This book was released on 2003 with total page 462 pages. Available in PDF, EPUB and Kindle. Book excerpt:
