scholarly journals On Refined Neutrosophic R-module

2020 ◽  
pp. 87-96
Author(s):  
Necati Olgun ◽  
◽  
◽  
Ahmed Hatip
Keyword(s):  
Structural Properties ◽  
Algebraic Structure ◽  
Binary Operations ◽  
Module Homomorphism

Modules are one of the fundamental and rich algebraic structure concerning some binary operations in the study of algebra. In this paper, some basic structures of refined neutrosophic R-modules and refined neutrosophic submodules in algebra are generalized. Some properties of refined neutrosophic R-modules and refined neutrosophic submodules are presented. More precisely, classical modules and refined neutrosophic rings are utilized. Consequently, refinedneutrosophic R- modules that are completely different from the classical modular in the structural properties are introduced. Also, neutrosophic R-module homomorphism is explained and some definitions and theorems are presented.

scholarly journals On the generalization of Conway algebra

2018 ◽  
Vol 27 (02) ◽  
pp. 1850014 ◽  
Author(s):  
Seongjeong Kim
Keyword(s):  
Algebraic Structure ◽  
The Other ◽  
Second Step ◽  
Polynomial Invariant ◽  
Binary Operations ◽  
Other Hand ◽  
Skein Relation

In [Przytyski and Traczyk, Invariants of links of Conway type, Kobe J. Math. 4 (1989) 115–139], Przytyski and Traczyk introduced an algebraic structure, called a Conway algebra, and constructed an invariant of oriented links, which is a generalization of the Homflypt polynomial invariant. On the other hand, in [Kauffman and Lambropoulou, New invariants of links and their state sum models, arXiv:1703.03655v2 [math.GT] 15 Mar 2017], Kauffman and Lambropoulou introduced new 4-variable invariants of oriented links, which are obtained by two computational steps: in the first step, we apply a skein relation on every mixed crossing to produce unions of unlinked knots. In the second step, we apply another skein relation on crossings of the unions of unlinked knots, which introduces a new variable. In this paper, we will introduce a generalization of the Conway algebra [Formula: see text] with two binary operations and we construct an invariant valued in [Formula: see text] by applying those two binary operations to mixed crossings and pure crossing, respectively. The 4-variable invariant of Kauffman and Lambropoulou with a specific condition is derived from the invariant valued in [Formula: see text]. Moreover, the generalized Conway algebra gives us an invariant of oriented links, which satisfies nonlinear skein relations.

Generalizations of a Conway algebra for oriented surface-links via marked graph diagrams

2018 ◽  
Vol 27 (13) ◽  
pp. 1842014
Author(s):  
Yongju Bae ◽  
Seonmi Choi ◽  
Seongjeong Kim
Keyword(s):  
Algebraic Structure ◽  
Polynomial Invariant ◽  
Oriented Surface ◽  
Binary Operations ◽  
Marked Graphs ◽  
Marked Graph

In 1987, Przytyski and Traczyk introduced an algebraic structure, called a Conway algebra, and constructed an invariant of oriented links, which is a generalization of the HOMFLY-PT polynomial invariant. In 2018, Kim generalized a Conway algebra, which is an algebraic structure with two skein relations, which is called a generalized Conway algebra. In 2017, Joung, Kamada, Kawauchi and Lee constructed a polynomial invariant of oriented surface-links by using marked graph diagrams. In this paper, we will introduce generalizations [Formula: see text] and [Formula: see text] of a Conway algebra and a generalized Conway algebra, which are called a marked Conway algebra and a generalized marked Conway algebra, respectively. We will construct invariants valued in [Formula: see text] and [Formula: see text] for oriented marked graphs and oriented surface-links by applying binary operations to classical crossings and marked vertices via marked graph diagrams. The polynomial invariant of oriented surface-links is obtained from the invariant valued in the marked Conway algebra with additional conditions.

scholarly journals MENGKONSTRUKSI DIRECT PRODUCT NEAR RING DAN SMARANDACHE NEAR RING

2019 ◽  
Vol 2 (2) ◽  
pp. 70
Author(s):  
Rizky Muhammad Bagas ◽  
Titi Udjiani SRRM ◽  
Harjito Harjito
Keyword(s):  
Direct Product ◽  
Algebraic Structure ◽  
Cartesian Product ◽  
Direct Products ◽  
Cartesian Products ◽  
Binary Operations ◽  
Products Of Groups

If we have two arbitrary non empty sets  ,then their cartesian product can be constructed. Cartesian products of two sets can be generalized into  number of  sets. It has been found that if the algebraic structure of groups and rings are seen as any set, then the phenomenon of cartesian products of  sets  can be extended to groups and rings. Direct products of groups and rings can be obtained by adding binary operations to the cartesian product. This paper answers the question of whether the direct product phenomenon of groups and rings can also be extended at the  near ring and Smarandache near ring ?. The method in this paper is  by following the method in groups and rings, namely by seen that  near ring and Smarandache near ring  as a set and then build their cartesian products. Next,  the binary operations is adding to the cartesian  products that have been obtained to build the direct product definitions of near ring and near ring Smarandache.

scholarly journals Convexity of sets in metric Abelian groups

2020 ◽  
Vol 32 (6) ◽  
pp. 1477-1486 ◽  
Author(s):  
Włodzimierz Fechner ◽  
Zsolt Páles
Keyword(s):  
Abelian Group ◽  
Structural Properties ◽  
Spectral Radius ◽  
Algebraic Structure ◽  
Abelian Groups ◽  
Invariant Metric ◽  
Translation Invariant ◽  
Basic Properties ◽  
The Family ◽  
Cancellation Theorem

AbstractIn the present paper, we introduce a new concept of convexity which is generated by a family of endomorphisms of an Abelian group. In Abelian groups, equipped with a translation invariant metric, we define the boundedness, the norm, the modulus of injectivity and the spectral radius of endomorphisms. Beyond the investigation of their properties, our first main goal is an extension of the celebrated Rådström cancellation theorem. Another result generalizes the Neumann invertibility theorem. Next we define the convexity of sets with respect to a family of endomorphisms, and we describe the set-theoretical and algebraic structure of the class of such sets. Given a subset, we also consider the family of endomorphisms that make this subset convex, and we establish the basic properties of this family. Our first main result establishes conditions which imply midpoint convexity. The next main result, using our extension of the Rådström cancellation theorem, presents further structural properties of the family of endomorphisms that make a subset convex.

Newborn's Preference for Faces

1996 ◽  
Vol 1 (3) ◽  
pp. 200-205 ◽  
Author(s):  
Carlo Umiltà ◽  
Francesca Simion ◽  
Eloisa Valenza
Keyword(s):  
Visual System ◽  
Structural Properties ◽  
Sensory Properties ◽  
Human Face ◽  
System Experiment ◽  
Face Experiment

Four experiments were aimed at elucidating some aspects of the preference for facelike patterns in newborns. Experiment 1 showed a preference for a stimulus whose components were located in the correct arrangement for a human face. Experiment 2 showed a preference for stimuli that had optimal sensory properties for the newborn visual system. Experiment 3 showed that babies directed their attention to a facelike pattern even when it was presented simultaneously with a non-facelike stimulus with optimal sensory properties. Experiment 4 showed the preference for facelike patterns in the temporal hemifield but not in the nasal hemifield. It was concluded that newborns' preference for facelike patterns reflects the activity of a subcortical system which is sensitive to the structural properties of the stimulus.

Investigation of the structural properties of crystallized Fe-(Cu)-Sm-B ribbons

1998 ◽  
Vol 08 (PR2) ◽  
pp. Pr2-47-Pr2-50
Author(s):  
O. Crisan ◽  
J. M. Le Breton ◽  
F. Machizaud ◽  
A. Jianu ◽  
J. Teillet ◽  
...  
Keyword(s):  
Structural Properties
Sign in / Sign up

Export Citation Format

Share Document