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1 – 3 of 3Mohammed H. Fahmy, Ahmed Ageeb Elokl and Ramy Abdel-Khalek
The aim of this paper is to investigate the relationship between the ring structure of the twisted partial skew generalized power series ring
Abstract
Purpose
The aim of this paper is to investigate the relationship between the ring structure of the twisted partial skew generalized power series ring
Design/methodology/approach
The authors first introduce the history and motivation of this paper. Secondly, the authors give a brief exposition of twisted partial skew generalized power series ring, in addition to presenting some properties of such structure, for instance, a-rigid ring, a-compatible ring and (G,a)-McCoy ring. Finally, the study’s main results are stated and proved.
Findings
The authors establish the relation between the diameter and girth of the zero-divisor graph of twisted partial skew generalized power series ring
Originality/value
The results of the twisted partial skew generalized power series ring embrace a wide range of results of classical ring theoretic extensions, including Laurent (skew Laurent) polynomial ring, Laurent (skew Laurent) power series ring and group (skew group) ring and of course their partial skew versions.
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Keywords
Bikash Barman and Kukil Kalpa Rajkhowa
The authors study the interdisciplinary relation between graph and algebraic structure ring defining a new graph, namely “non-essential sum graph”. The nonessential sum graph…
Abstract
Purpose
The authors study the interdisciplinary relation between graph and algebraic structure ring defining a new graph, namely “non-essential sum graph”. The nonessential sum graph, denoted by NES(R), of a commutative ring R with unity is an undirected graph whose vertex set is the collection of all nonessential ideals of R and any two vertices are adjacent if and only if their sum is also a nonessential ideal of R.
Design/methodology/approach
The method is theoretical.
Findings
The authors obtain some properties of NES(R) related with connectedness, diameter, girth, completeness, cut vertex, r-partition and regular character. The clique number, independence number and domination number of NES(R) are also found.
Originality/value
The paper is original.
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Keywords
Dinghe Guo, Xiaolu Zhou, Jinghong Pan and Zhangbo Guo
To develop an overview of generalized scales based on pansystems‐relative quantification.
Abstract
Purpose
To develop an overview of generalized scales based on pansystems‐relative quantification.
Design/methodology/approach
This is a discussion paper exploring the key issues surrounding generalized measures.
Findings
The concrete contents of the study include generalized measure views, dimension theory, concepts, logic, theories, Einstein's relativity, quality‐quantity‐degree, methodology of physics, theorems in pansystems mathematics and physics explained within the framework of pan‐scale transformations.
Originality/value
Provides an overview of generalized scales based on pansystems‐relative quantification.
Details