Some Commutativity Theorems for Prime Near-rings Involving Derivations
Journal Title: Journal of Advances in Mathematics and Computer Science - Year 2017, Vol 25, Issue 6
Abstract
The study depicts that a prime near-ring is considered to be a commutative ring if there non-negative integers exist i.e., p≥0,q≥0 in such a way that admits a non-zero derivation, where satisfying one of the conditions like (c_1)-〖(c〗_8). For any x,y∈N, we define the following properties (c_1) d([x,y])-x^p (xoy) x^q=0 ; 〖(c〗_2) d([x,y])+x^p (xoy) x^q=0 ; (c_3) d(xoy)-x^p ([x,y] ) x^q=0 ; 〖(c〗_4) d(xoy)+x^p ([x,y]) x^q=0 ; (c_5) d([x,y])-y^p (xoy) y^q=0 ; 〖(c〗_6) d([x,y])+y^p (xoy) y^q=0; (c_7) d(xoy)-y^p ([x,y]) y^q=0 ; 〖(c〗_8) d(xoy)+y^p ([x,y]) y^q=0. In addition, an example is given to demonstrate the primeness of the hypothesis which is not superfluous. Finally, we can conclude it with some open problems.
Authors and Affiliations
Moharram A. Khan, Abdu Madugu
Keywords
Related Articles
- EP ID EP322604
- DOI 10.9734/JAMCS/2017/38097
- Views 88
- Downloads 0
mcga: R Implementation of the Machine-coded Genetic Algorithms
Genetic Algorithms (GAs) are global optimization and search algorithms that mimic the natural selection and genetic processes. Floating-point GAs (FPGAs) are other type of GAs which directly operate on real-vectors witho...
Recurrent Neural Network Based Modeling of Gene Regulatory Network Using Bat Algorithm
Correct inference of genetic regulations inside a cell is one of the greatest challenges in post genomic era for the biologist and researchers. Several intelligent techniques and models were already proposed to identify...
A New Structure and Contribution in D-metric Spaces
In this paper, we define a new topological structure of D-closed, D-continuous and D-fixed point property and discussed of its properties, some result for this subject are also established.
Mathematical Model of Drinking Epidemic
A non-linear SHTR mathematical model was used to study the dynamics of drinking epidemic. We discussed the existence and stability of the drinking-free and endemic equilibria. The drinking-free equilibrium was locally as...
A Conceptual Approach to Resources Allocation Scheduling
The problem of scheduling and allocation of resources, both space and time, has generated a lot of issues and has become of great concerns in daily human activities. The choice of best or appropriate computational algori...