scholarly journals A Note on Neutrosophic Submodule of an R-module M

2020 ◽  
pp. 118-127
Author(s):  
Binu R ◽  
Keyword(s):  
Set Theory ◽  
Neutrosophic Set ◽  
Sufficient Condition ◽  
Algebraic Structures ◽  
Necessary And Sufficient Condition ◽  
Neutrosophic Sets ◽  
Algebraic Operations ◽  
Necessary And Sufficient

The paper focuses on the applications of neutrosophic set theory in the domain of classical algebraic structures, especially R-module. This study discusses some algebraic operations of neutrosophic sets of an R-moduleM, induced by the operations in M and demonstrates certain properties of the neutrosophic submodules of an R-module. The ideas of R module’s non-empty arbitrary family of neutrosophic submodules are characterized, and related outcomes are proved. The last section of this paper also derives a necessary and sufficient condition for a neutrosophic set of an R-module M.

scholarly journals Quasi-trivial quandles and biquandles, cocycle enhancements and link-homotopy of pretzel links

2018 ◽  
Vol 27 (11) ◽  
pp. 1843007
Author(s):  
Mohamed Elhamdadi ◽  
Minghui Liu ◽  
Sam Nelson
Keyword(s):  
Homotopy Type ◽  
Knot Theory ◽  
Sufficient Condition ◽  
Algebraic Structures ◽  
Necessary And Sufficient Condition ◽  
Link Homotopy ◽  
Necessary And Sufficient

We investigate some algebraic structures called quasi-trivial quandles and we use them to study link-homotopy of pretzel links. Precisely, a necessary and sufficient condition for a pretzel link with at least two components being trivial under link-homotopy is given. We also generalize the quasi-trivial quandle idea to the case of biquandles and consider enhancement of the quasi-trivial biquandle cocycle counting invariant by quasi-trivial biquandle cocycles, obtaining invariants of link-homotopy type of links analogous to the quasi-trivial quandle cocycle invariants in Inoue’s paper [A. Inoue, Quasi-triviality of quandles for link-homotopy, J. Knot Theory Ramifications 22(6) (2013) 1350026, doi:10.1142/S0218216513500260, MR3070837].

scholarly journals Extensions with Abelian Kernels in Protomodular Categories

2004 ◽  
Vol 11 (4) ◽  
pp. 645-654
Author(s):  
D. Bourn ◽  
G. Janelidze
Keyword(s):  
Sufficient Condition ◽  
Algebraic Structures ◽  
Necessary And Sufficient Condition ◽  
Joint Work ◽  
Group Extensions ◽  
Protomodular Category ◽  
Necessary And Sufficient

Abstract As observed by J. Beck, and as we know from M. Barr's and his joint work on triple cohomology, the classical isomorphism Opext ≅ 𝐻2 that describes group extensions with abelian kernels, can be deduced from the equivalence between such extensions and torsors (in an appropriate sense). The same is known for many other “group-like” algebraic structures, and now we present a purely-categorical version of that equivalence, essentially by showing that all torsors are extensions with abelian kernels in any pointed protomodular category, and by giving a necessary and sufficient condition for the converse.

scholarly journals Single valued neutrosophic $ (m, n) $-ideals of ordered semirings

2021 ◽  
Vol 7 (1) ◽  
pp. 1211-1223
Author(s):  
Saba Al-Kaseasbeh ◽  
◽  
Madeline Al Tahan ◽  
Bijan Davvaz ◽  
Mariam Hariri ◽  
...  
Keyword(s):  
Level Sets ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Neutrosophic Sets ◽  
Necessary And Sufficient ◽  
Innovative Concept

<abstract><p>The aim of this paper is to combine the innovative concept of single valued neutrosophic sets and ordered semirings. It studies ordered semirings by the properties of their single valued neutrosphic subsets. In this regard, we define single valued neutrosophic $ (m, n) $-ideals (SVN-$ (m, n) $-ideals) of ordered semirings. First, we illustrate our new definition by non-trivial examples. Second, we study these SVN-$ (m, n) $-ideals under different operations of SVNS. Finally, we find a relationship between the $ (m, n) $-ideals of ordered semirings and level sets by finding a necessary and sufficient condition for an SVNS of an ordered semiring $ R $ to be an SVN-$ (m, n) $-ideal of $ R $.</p></abstract>

A Proposed Framework Emphasizing Auditor Reliability over Auditor Independence

2003 ◽  
Vol 17 (3) ◽  
pp. 257-266 ◽  
Author(s):  
Mark H. Taylor ◽  
F. Todd DeZoort ◽  
Edward Munn ◽  
Martha Wetterhall Thomas
Keyword(s):  
Public Interest ◽  
Auditor Independence ◽  
Public Confidence ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Accounting Profession ◽  
The Public ◽  
Necessary And Sufficient

This paper introduces an auditor reliability framework that repositions the role of auditor independence in the accounting profession. The framework is motivated in part by widespread confusion about independence and the auditing profession's continuing problems with managing independence and inspiring public confidence. We use philosophical, theoretical, and professional arguments to argue that the public interest will be best served by reprioritizing professional and ethical objectives to establish reliability in fact and appearance as the cornerstone of the profession, rather than relationship-based independence in fact and appearance. This revised framework requires three foundation elements to control subjectivity in auditors' judgments and decisions: independence, integrity, and expertise. Each element is a necessary but not sufficient condition for maximizing objectivity. Objectivity, in turn, is a necessary and sufficient condition for achieving and maintaining reliability in fact and appearance.

The Power of Public Positions

2018 ◽  
Author(s):  
Thomas Sinclair
Keyword(s):  
Detailed Analysis ◽  
Political Authority ◽  
The State ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
State Institutions ◽  
State Of Nature ◽  
Necessary And Sufficient

The Kantian account of political authority holds that the state is a necessary and sufficient condition of our freedom. We cannot be free outside the state, Kantians argue, because any attempt to have the “acquired rights” necessary for our freedom implicates us in objectionable relations of dependence on private judgment. Only in the state can this problem be overcome. But it is not clear how mere institutions could make the necessary difference, and contemporary Kantians have not offered compelling explanations. A detailed analysis is presented of the problems Kantians identify with the state of nature and the objections they face in claiming that the state overcomes them. A response is sketched on behalf of Kantians. The key idea is that under state institutions, a person can make claims of acquired right without presupposing that she is by nature exceptional in her capacity to bind others.

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