Smarandache Be Algebras
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Smarandache BE Algebras
Author | : Arsham Borumand Saeid |
Publsiher | : Infinite Study |
Total Pages | : 65 |
Release | : 2024 |
Genre | : Electronic Book |
ISBN | : 9781599732411 |
Download Smarandache BE Algebras Book in PDF, Epub and Kindle
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.
Smarandache pseudo CI algebras
Author | : L. C. Ciungu, A. Rezaei, A. Radfar |
Publsiher | : Infinite Study |
Total Pages | : 18 |
Release | : 2024 |
Genre | : Mathematics |
ISBN | : 9182736450XXX |
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In this paper, we define the notion of Smarandache pseudo-CI algebras and we investigate their properties. We also define and study the notions of Smarandache filters, pseudo-CI Smarandache homomorphisms and modal Smarandache operators on pseudo-CI algebras.
Algebras and Smarandache Types
Author | : Hee Sik Kim,J. Neggers,Sun Shin Ahn |
Publsiher | : Infinite Study |
Total Pages | : 6 |
Release | : 2018-01-01 |
Genre | : Mathematics |
ISBN | : 9182736450XXX |
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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.
Smarandache n Structure on CI Algebras
Author | : Arsham Borumand Saeid,Akbar Rezaei |
Publsiher | : Infinite Study |
Total Pages | : 11 |
Release | : 2024 |
Genre | : Mathematics |
ISBN | : 9182736450XXX |
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In this paper, the notions of CI-algebras, Smarandache CI-algebra, Q-Smarandache filters and Q-Smarandache ideals are introduced. Finally, we introduced the concepts of Smarandache BE-algebra, Smarandache dual BCK-algebra and Smarandache n-structure on CI-algebra.
Smarandache Fuzzy Algebra
Author | : W. B. Vasantha Kandasamy |
Publsiher | : Infinite Study |
Total Pages | : 455 |
Release | : 2003 |
Genre | : Mathematics |
ISBN | : 9781931233743 |
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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.
Q Smarandache Fuzzy Implicative Ideal of QSmarandache BH Algebra
Author | : Husein Hadi Abbass,Qasim Mohsin Luhaib |
Publsiher | : Infinite Study |
Total Pages | : 15 |
Release | : 2024 |
Genre | : Mathematics |
ISBN | : 9182736450XXX |
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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.
Linear Algebra and Smarandache Linear Algebra
Author | : W. B. Vasantha Kandasamy |
Publsiher | : Infinite Study |
Total Pages | : 175 |
Release | : 2003 |
Genre | : Mathematics |
ISBN | : 9781931233750 |
Download Linear Algebra and Smarandache Linear Algebra Book in PDF, Epub and Kindle
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.
On Smarandache Filter of a Smarandache BH Algebra
Author | : Husein Hadi Abbass,Qasim Mohsin Luhaib |
Publsiher | : Infinite Study |
Total Pages | : 7 |
Release | : 2024 |
Genre | : Mathematics |
ISBN | : 9182736450XXX |
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In this paper, The notion of a Smarandache filter of a Smarandache BHAlgebra is introduced, some theorems and examples are investigated and discussed to explain properties of this notion. A necessary and sufficient condition is derived for every Smarandache filter of a Smarandache BH-Algebra to become a filter. Finally, the relationships between this notion and Smarandache ideal are established.