THE SMARANDACHE VERTICES OF THE COMAXIMAL GRAPH OF A COMMUTATIVE RING PDF Download
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Author: ELHAM MEHDI-NEZHAD
Publisher: Infinite Study
ISBN:
Category : Mathematics
Languages : en
Pages : 12
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Book Description
The concept of a Smarandache vertex (or S-vertex for short) in a (simple) graph (Definition 2.5) was first introduced by the second author [8] in order to study the Smarandache zero-divisors of a commutative ring which was introduced by Vasantha Kandasamy in [10] for semigroups and rings (not necessarily commutative).
Author: ELHAM MEHDI-NEZHAD
Publisher: Infinite Study
ISBN:
Category : Mathematics
Languages : en
Pages : 12
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Book Description
The concept of a Smarandache vertex (or S-vertex for short) in a (simple) graph (Definition 2.5) was first introduced by the second author [8] in order to study the Smarandache zero-divisors of a commutative ring which was introduced by Vasantha Kandasamy in [10] for semigroups and rings (not necessarily commutative).
Author: ELHAM MEHDI-NEZHAD
Publisher: Infinite Study
ISBN:
Category : Mathematics
Languages : en
Pages : 12
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Book Description
The main object of this paper is to study the S-vertices of CG(R) and CG2(R) \ J(R) (or CGJ (R) for short), where CG2(R) is the subgraph of CG(R) which consists of nonunit elements of R and J(R) is the Jacobson radical of R. There is also a discussion on a relationship between the diameter and S-vertices of CGJ (R).
Author: Subramanian Visweswaran
Publisher: Infinite Study
ISBN:
Category :
Languages : en
Pages : 15
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Book Description
The rings considered in this article are commutative with identity which admit at least two maximal ideals. Let R be a ring such that R admits at least two maximal ideals.
Author: Marco Fontana
Publisher: Springer Science & Business Media
ISBN: 144196990X
Category : Mathematics
Languages : en
Pages : 491
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Book Description
Commutative algebra is a rapidly growing subject that is developing in many different directions. This volume presents several of the most recent results from various areas related to both Noetherian and non-Noetherian commutative algebra. This volume contains a collection of invited survey articles by some of the leading experts in the field. The authors of these chapters have been carefully selected for their important contributions to an area of commutative-algebraic research. Some topics presented in the volume include: generalizations of cyclic modules, zero divisor graphs, class semigroups, forcing algebras, syzygy bundles, tight closure, Gorenstein dimensions, tensor products of algebras over fields, as well as many others. This book is intended for researchers and graduate students interested in studying the many topics related to commutative algebra.
![Smarandache Geometries & Map Theories with Applications (I) [English and Chinese] PDF](https://books.google.com/books/content/images/frontcover/fR7eBAAAQBAJ?fife=w80-h100)
Author: Linfan Mao
Publisher: Infinite Study
ISBN: 1599730197
Category : Mathematics
Languages : en
Pages : 215
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Book Description
800x600 Normal 0 false false false EN-US X-NONE X-NONE MicrosoftInternetExplorer4 /* 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:0in; mso-para-margin-bottom:.0001pt; mso-pagination:widow-orphan; font-size:10.0pt; font-family:"Times New Roman","serif";} Smarandache Geometries as generalizations of Finsler, Riemannian, Weyl, and Kahler Geometries. A Smarandache geometry (SG) is a geometry which has at least one smarandachely denied axiom (1969). An axiom is said smarandachely denied (S-denied) if in the same space the axiom behaves differently (i.e., validated and invalided; or only invalidated but in at least two distinct ways). Thus, as a particular case, Euclidean, Lobachevsky-Bolyai-Gauss, and Riemannian geometries may be united altogether, in the same space, by some SGs. These last geometries can be partially Euclidean and partially non-Euclidean. The novelty of the SG is the fact that they introduce for the first time the degree of negation in geometry, similarly to the degree of falsehood in fuzzy or neutrosophic logic. For example an axiom can be denied in percentage of 30 Also SG are defined on multispaces, i.e. unions of Euclidean and non-Euclidean subspaces, or unions of distinct non-Euclidean spaces. As an example of S-denying, a proposition , which is the conjunction of a set i of propositions, can be invalidated in many ways if it is minimally unsatisfiable, that is, such that the conjunction of any proper subset of the i is satisfied in a structure, but itself is not. Here it is an example of what it means for an axiom to be invalidated in multiple ways [2] : As a particular axiom let's take Euclid's Fifth Postulate. In Euclidean or parabolic geometry a line has one parallel only through a given point. In Lobacevskian or hyperbolic geometry a line has at least two parallels through a given point. In Riemannian or elliptic geometry a line has no parallel through a given point. Whereas in Smarandache geometries there are lines which have no parallels through a given point and other lines which have one or more parallels through a given point (the fifth postulate is invalidated in many ways). Therefore, the Euclid's Fifth Postulate (which asserts that there is only one parallel passing through an exterior point to a given line) can be invalidated in many ways, i.e. Smarandachely denied, as follows: - first invalidation: there is no parallel passing through an exterior point to a given line; - second invalidation: there is a finite number of parallels passing through an exterior point to a given line; - third invalidation: there are infinitely many parallels passing through an exterior point to a given line.
Author: Javad Mashreghi
Publisher: American Mathematical Soc.
ISBN: 9780821848791
Category : Mathematics
Languages : en
Pages : 0
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Book Description
Hilbert spaces of analytic functions are currently a very active field of complex analysis. The Hardy space is the most senior member of this family. However, other classes of analytic functions such as the classical Bergman space, the Dirichlet space, the de Branges-Rovnyak spaces, and various spaces of entire functions, have been extensively studied. This provides an account of the latest developments in the field of analytic function theory.
Author: Inder Bir Singh Passi
Publisher: Springer
ISBN: 9811328951
Category : Mathematics
Languages : en
Pages : 231
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Book Description
The book describes developments on some well-known problems regarding the relationship between orders of finite groups and that of their automorphism groups. It is broadly divided into three parts: the first part offers an exposition of the fundamental exact sequence of Wells that relates automorphisms, derivations and cohomology of groups, along with some interesting applications of the sequence. The second part offers an account of important developments on a conjecture that a finite group has at least a prescribed number of automorphisms if the order of the group is sufficiently large. A non-abelian group of prime-power order is said to have divisibility property if its order divides that of its automorphism group. The final part of the book discusses the literature on divisibility property of groups culminating in the existence of groups without this property. Unifying various ideas developed over the years, this largely self-contained book includes results that are either proved or with complete references provided. It is aimed at researchers working in group theory, in particular, graduate students in algebra.
Author: R. Balakrishnan
Publisher: Springer Science & Business Media
ISBN: 1461445280
Category : Mathematics
Languages : en
Pages : 296
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Book Description
In its second edition, expanded with new chapters on domination in graphs and on the spectral properties of graphs, this book offers a solid background in the basics of graph theory. Introduces such topics as Dirac's theorem on k-connected graphs and more.
Author: Bijan Davvaz
Publisher: Academic Press
ISBN: 0128099259
Category : Mathematics
Languages : en
Pages : 166
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Book Description
Semihypergroup Theory is the first book devoted to the semihypergroup theory and it includes basic results concerning semigroup theory and algebraic hyperstructures, which represent the most general algebraic context in which reality can be modelled. Hyperstructures represent a natural extension of classical algebraic structures and they were introduced in 1934 by the French mathematician Marty. Since then, hundreds of papers have been published on this subject. - Offers the first book devoted to the semihypergroup theory - Presents an introduction to recent progress in the theory of semihypergroups - Covers most of the mathematical ideas and techniques required in the study of semihypergroups - Employs the notion of fundamental relations to connect semihypergroups to semigroups
Author: Linfan Mao
Publisher: Infinite Study
ISBN: 159973155X
Category : Combinatorial geometry
Languages : en
Pages : 502
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Book Description
