254 research outputs found

    Smarandache Near-rings

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    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 contained 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 Near-ring is a non-empty set N together with two binary operations '+' and '.' such that (N, +) is a group (not necessarily abelian), (N, .) is a semigroup. For all a, b, c belonging to N we have (a + b) . c = a . c + b . c A Near-field is a non-empty set P together with two binary operations '+' and '.' such that (P, +) is a group (not-necessarily abelian), {P\{0}, .) is a group. For all a, b, c belonging to P we have (a + b) . c = a . c + b . c A Smarandache Near-ring is a near-ring N which has a proper subset P contained in N, where P is a near-field (with respect to the same binary operations on N).Comment: 200 pages, 50 tables, 20 figure

    Neutrosophic Left Almost Semigroup

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    In this paper we extend the theory of neutrosophy to study left almost semigroup shortly LAsemigroup. We generalize the concepts of LA-semigroup to form that for neutrosophic LA-semigroup. We also extend the ideal theory of LA-semigroup to neutrosophy and discuss different kinds of neutrosophic ideals. We also find some new type of neutrosophic ideal which is related to the strong or pure part of neutrosophy. We have given many examples to illustrate the theory of neutrosophic LA-semigroup and display many properties of neutrosophic LA-semigroup in this paper

    Smarandache near-rings

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    The main concern of this book is the study of Smarandache analogue properties of near-rings and Smarandache near-rings; so it does not promise to cover all concepts or the proofs of all results

    Theoretical Computer Science and Discrete Mathematics

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    This book includes 15 articles published in the Special Issue "Theoretical Computer Science and Discrete Mathematics" of Symmetry (ISSN 2073-8994). This Special Issue is devoted to original and significant contributions to theoretical computer science and discrete mathematics. The aim was to bring together research papers linking different areas of discrete mathematics and theoretical computer science, as well as applications of discrete mathematics to other areas of science and technology. The Special Issue covers topics in discrete mathematics including (but not limited to) graph theory, cryptography, numerical semigroups, discrete optimization, algorithms, and complexity

    New Research on Neutrosophic Algebraic Structures

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    In this book, we define several new neutrosophic algebraic structures and their related properties. The main focus of this book is to study the important class of neutrosophic rings such as neutrosophic LA-semigroup ring, neutrosophic loop ring, neutrosophic groupoid ring and so on. We also construct their generalization in each case to study these neutrosophic algebraic structures in a broader sense. The indeterminacy element “ I “ gives rise to a more bigger algebraic structure than the classical algebraic structures. It mainly classifies the algebraic structures in three categories: such as neutrosophic algebraic structures, strong neutrosophic algebraic structures, and classical algebraic structures respectively. This reveals the fact that a classical algebraic structure is a part of the neutrosophic algebraic structures. This opens a new way for the researchers to think in a broader way to visualize these vast neutrosophic algebraic structures. This book is a small attempt to do this job

    Problems on MOD Structures

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    In this book authors for the first time give several types of problems on MOD structures happens to be an interesting field of study as it makes the whole 4 quadrant plane into a single quadrant plane and the infinite line into a half closed open interval. So study in this direction will certainly yield several interesting results. The law of distributivity is not true. Further the MOD function in general do not obey all the laws of integration or differentiation. Likewise MOD polynomials in general do not satisfy the basic properties of polynomials like its roots etc. Thus over all this study is not only innovative and interesting but challenging. So this book which is only full of problems based on MOD structures will be a boon to researchers. Further the MOD series books of the authors will certainly be an appropriate guide to solve these problems

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    Karakteristik Invarian Translasional Subhimpunan Fuzzy Relatif terhadap Homomorfisma Ring

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    Diawali dengan pendefinisian invarian translasional suatu subhimpunan fuzzy pada sebarang himpunan yang di dalamnya dilengkapi dengan operasi biner, selanjutnya definisi ini secara khusus didefinisikan juga pada subhimpunan fuzzy pada ring. Dengan demikian definisi invarian translasional tersebut didefinisikan relatif terhadap operasi penjumlahan dan pergandaan pada ring. Berdasarkan definisi image f ( μ ) dan pre-image f −1 ( φ ) , dengan f adalah pemetaan dari ring R ke R ' , μ dan φ masing-masing adalah subhimpunan fuzzy pada R dan R' , maka dalam tulisan ini akan dikaji karakteristik invarian translasional suatu subhimpunan fuzzy relatif terhadap homomorfisma ring, yaitu dengan menambah syarat khusus untuk f bukan hanya suatu pemetaan akan tetapi f merupakan suatu homomorfisma. Diperoleh hasil bahwa: jika f homomorfisma dari ring R ke R' dan λ subhimpunan fuzzy invarian translasional pada R ' , maka f −1 (λ) subhimpunan fuzzy invarian translasional pada R . Misalkan f adalah homomorfisma surjektif dari ring R ke R ' dan λ subhimpunan fuzzy invarian translasional pada R . Jika λ adalah f -invarian, maka f (λ ) adalah subhimpunan fuzzy invarian translasional pada R ' . Akibat lain adalah f (I (a, λ ) ) = I ( f ( a), f (λ )) , untuk setiap a ∈ R . Untuk suatu a'∈ R' , maka untuk setiap a, b ∈ f −1 (a' ) , I (a, f −1 (λ )) = I (b, f −1 (λ )) Kata Kunci : subhimpunan fuzzy, invarian translasional, homomorfisma rin
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