Non-Associative Algebraic Structures on MOD Planes

Non-Associative Algebraic Structures on MOD Planes
Author: W. B. Vasantha Kandasamy
Publisher: Infinite Study
Total Pages: 212
Release: 2015
Genre: Algebras, Linear
ISBN: 1599733684

In this book authors for the first time construct non-associative algebraic structures on the MOD planes. Using MOD planes we can construct infinite number of groupoids for a fixed m and all these MOD groupoids are of infinite cardinality. Special identities satisfied by these MOD groupoids build using the six types of MOD planes are studied. Further, the new concept of special pseudo zero of these groupoids are defined, described and developed. Also conditions for these MOD groupoids to have special elements like idempotent, special pseudo zero divisors and special pseudo nilpotent are obtained. Further non-associative MOD rings are constructed using MOD groupoids and commutative rings with unit. That is the MOD groupoid rings gives infinitely many non-associative ring. These rings are analysed for substructures and special elements. This study is new and innovative and several open problems are suggested.

Interval Groupoids

Interval Groupoids
Author: W. B. Vasantha Kandasamy
Publisher: Infinite Study
Total Pages: 242
Release: 2010
Genre: Mathematics
ISBN: 1599731258

This book defines new classes of groupoids, like matrix groupoid, polynomial groupoid, interval groupoid, and polynomial groupoid.An interesting feature of this book is that introduces 77 new definitions substantiated and described by 426 examples and 150 theorems.

Theory of Abel Grassmann's Groupoids

Theory of Abel Grassmann's Groupoids
Author: Madad Khan, Florentin Smarandache, Saima Anis
Publisher: Infinite Study
Total Pages: 210
Release: 2015-04-01
Genre: Fuzzy sets
ISBN: 1599733471

We extend now for the first time the AG-groupoid to the Neutrosophic AG-groupoid. A neutrosophic AG-groupoid is a neutrosophic algebraic structure that lies between a neutrosophic groupoid and a neutrosophic commutative semigroup.

The Encyclopedia of Neutrosophic Researchers, 1st volume

The Encyclopedia of Neutrosophic Researchers, 1st volume
Author: Florentin Smarandache
Publisher: Infinite Study
Total Pages: 232
Release: 2016-11-12
Genre: Mathematics
ISBN: 1599734680

This is the first volume of the Encyclopedia of Neutrosophic Researchers, edited from materials offered by the authors who responded to the editor’s invitation. The 78 authors are listed alphabetically. The introduction contains a short history of neutrosophics, together with links to the main papers and books. Neutrosophic set, neutrosophic logic, neutrosophic probability, neutrosophic statistics, neutrosophic measure, neutrosophic precalculus, neutrosophic calculus and so on are gaining significant attention in solving many real life problems that involve uncertainty, impreciseness, vagueness, incompleteness, inconsistent, and indeterminacy. In the past years the fields of neutrosophics have been extended and applied in various fields, such as: artificial intelligence, data mining, soft computing, decision making in incomplete / indeterminate / inconsistent information systems, image processing, computational modelling, robotics, medical diagnosis, biomedical engineering, investment problems, economic forecasting, social science, humanistic and practical achievements.

Groupoids of Type I and II Using [0, n)

Groupoids of Type I and II Using [0, n)
Author: W. B. Vasantha Kandasamy
Publisher: Infinite Study
Total Pages: 180
Release: 2014
Genre: Mathematics
ISBN: 1599732734

Study of algebraic structures built using [0, n) looks to be one of interesting and innovative research. Here we define two types of groupoids using [0, n), both of them are of infinite order. It is an open conjecture to find whether this new class of groupoids satisfy any of the special identities like Moufang identity or Bol identity and so on.

Hyperbolic Groupoids and Duality

Hyperbolic Groupoids and Duality
Author: Volodymyr Nekrashevych
Publisher: American Mathematical Soc.
Total Pages: 120
Release: 2015-08-21
Genre: Mathematics
ISBN: 1470415445

The author introduces a notion of hyperbolic groupoids, generalizing the notion of a Gromov hyperbolic group. Examples of hyperbolic groupoids include actions of Gromov hyperbolic groups on their boundaries, pseudogroups generated by expanding self-coverings, natural pseudogroups acting on leaves of stable (or unstable) foliation of an Anosov diffeomorphism, etc. The author describes a duality theory for hyperbolic groupoids. He shows that for every hyperbolic groupoid G there is a naturally defined dual groupoid G⊤ acting on the Gromov boundary of a Cayley graph of G. The groupoid G⊤ is also hyperbolic and such that (G⊤)⊤ is equivalent to G. Several classes of examples of hyperbolic groupoids and their applications are discussed.

Soft Neutrosophic Groupoids and Their Generalization

Soft Neutrosophic Groupoids and Their Generalization
Author: Mumtaz Ali
Publisher: Infinite Study
Total Pages: 20
Release:
Genre:
ISBN:

Soft set theory is a general mathematical tool for dealing with uncertain, fuzzy, not clearly defined objects. In this paper we introduced soft neutrosophic groupoid and their generalization with the discuissionf of some of their characteristics