Smarandache N Structure On Ci Algebras
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Smarandache N Structure On Ci Algebras
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Author : Arsham Borumand Saeid
language : en
Publisher: Infinite Study
Release Date :
Smarandache N Structure On Ci Algebras written by Arsham Borumand Saeid and has been published by Infinite Study this book supported file pdf, txt, epub, kindle and other format this book has been release on with Mathematics categories.
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 Be Algebras
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Author : Arsham Borumand Saeid
language : en
Publisher: Infinite Study
Release Date :
Smarandache Be Algebras written by Arsham Borumand Saeid and has been published by Infinite Study this book supported file pdf, txt, epub, kindle and other format this book has been release on with categories.
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
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Author : L. C. Ciungu
language : en
Publisher: Infinite Study
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Smarandache Pseudo Ci Algebras written by L. C. Ciungu and has been published by Infinite Study this book supported file pdf, txt, epub, kindle and other format this book has been release on with Mathematics categories.
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.
A New Trend To Extensions Of Ci Algebras
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Author : Florentin Smarandache
language : en
Publisher: Infinite Study
Release Date : 2020-05-14
A New Trend To Extensions Of Ci Algebras written by Florentin Smarandache and has been published by Infinite Study this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-05-14 with Antiques & Collectibles categories.
In this paper, as an extension of CI-algebras, we discuss the new notions of Neutro-CI-algebras and Anti-CI-algebras. First, some examples are given to show that these definitions are different. We prove that any proper CI-algebra is a Neutro-BE-algebra or Anti-BE-algebra. Also, we show that any NeutroSelf-distributive and AntiCommutative CIalgebras are not BE-algebras.
Smarandache N Subalgebras Resp Filters Of Ci Algebras
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Author : Akbar Rezaei
language : en
Publisher: Infinite Study
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Smarandache N Subalgebras Resp Filters Of Ci Algebras written by Akbar Rezaei and has been published by Infinite Study this book supported file pdf, txt, epub, kindle and other format this book has been release on with categories.
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.
Left Right Quasi Neutrosophic Triplet Loops Groups And Generalized Be Algebras
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Author : Xiaohong Zhang
language : en
Publisher: Infinite Study
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Left Right Quasi Neutrosophic Triplet Loops Groups And Generalized Be Algebras written by Xiaohong Zhang and has been published by Infinite Study this book supported file pdf, txt, epub, kindle and other format this book has been release on with categories.
The new notion of a neutrosophic triplet group (NTG) is proposed by Florentin Smarandache; it is a new algebraic structure different from the classical group.
N Algebraic Structures
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Author : W. B. Vasantha Kandasamy
language : en
Publisher: Infinite Study
Release Date : 2005-01-01
N Algebraic Structures written by W. B. Vasantha Kandasamy and has been published by Infinite Study this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005-01-01 with Mathematics categories.
In this book, for the first time we introduce the notions of N-groups, N-semigroups, N-loops and N-groupoids. We also define a mixed N-algebraic structure. The book is organized into six chapters. The first chapter gives the basic notions of S-semigroups, S-groupoids and S-loops thereby making the book self-contained. Chapter two introduces N-groups and their Smarandache analogues. In chapter three, N-loops and Smarandache N-loops are introduced and analyzed. Chapter four defines N-groupoids and S-N-groupoids. Since the N-semigroup structures are sandwiched between groups and groupoids, the study can be carried out without any difficulty. Mixed N-algebraic structures and S-mixed algebraic structures are given in chapter five. Some problems are suggested in chapter six. It is pertinent to mention that several exercises and problems (Some in the form of proof to the theorems are given in all the chapters.) A reader who attempts to solve them will certainly gain a sound knowledge about these concepts. We have given 50 problems for the reader to solve in chapter 6. The main aim of this book is to introduce new concepts and explain them with examples there by encouraging young mathematics to pursue research in this direction. Several theorems based on the definition can be easily proved with simple modification. Innovative readers can take up that job. Also these notions find their applications in automaton theory and coloring problems. The N-semigroups and N-automaton can be applied to construct finite machines, which can perform multitasks, so their capability would be much higher than the usual automaton of finite machines constructed. We have suggested a list of references for further reading.
Smarandache Pseudo Ci Algebras
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Author : L. C. Ciungu
language : en
Publisher: Infinite Study
Release Date : 2022-01-01
Smarandache Pseudo Ci Algebras written by L. C. Ciungu and has been published by Infinite Study this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-01-01 with Mathematics categories.
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. The classes of Smarandache fantastic, implicative and positive implicative filters of Smarandache pseudo-CI algebras are defined and studied by extending some results regarding Smarandache fantastic, fresh and clean ideals in Smarandache BCI-algebras and Smarandache BCH-algebras to the case of Smarandache pseudo-CI algebras. The notion of Smarandache commutative pseudo-CI algebras is defined and a characterization theorem is given. It is proved that in the case of commutative Q-Smarandache pseudo-CI algebras the notions of Smarandache filters and fantastic filters coincide.
Smarandache Special Definite Algebraic Structures
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Author : W. B. Vasantha Kandasamy
language : en
Publisher: Infinite Study
Release Date : 2009-01-01
Smarandache Special Definite Algebraic Structures written by W. B. Vasantha Kandasamy and has been published by Infinite Study this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-01-01 with Mathematics categories.
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.
Algebraic Structures Of Neutrosophic Triplets Neutrosophic Duplets Or Neutrosophic Multisets
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Author : Florentin Smarandache
language : en
Publisher: MDPI
Release Date : 2019-04-04
Algebraic Structures Of Neutrosophic Triplets Neutrosophic Duplets Or Neutrosophic Multisets written by Florentin Smarandache and has been published by MDPI this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-04-04 with Mathematics categories.
Neutrosophy (1995) is a new branch of philosophy that studies triads of the form (,