σ-Ideals in a 0-1 distributive lattice

2016 ◽  
Vol 09 (01) ◽  
pp. 1650025
Author(s):  
Y. S. Pawar ◽  
S. S. Khopade
Keyword(s):  
Distributive Lattice ◽  
Distributive Lattices ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Complemented Lattices ◽  
Necessary And Sufficient

The notion of a [Formula: see text]-ideal in a [Formula: see text]-[Formula: see text] distributive lattice is introduced and studied. Certain classes of [Formula: see text]-[Formula: see text] distributive lattices such as normal lattices, complemented lattices, generalized Stone lattices are characterized by using the properties of [Formula: see text]-ideals. Stable ideals are defined and a necessary and sufficient condition for a [Formula: see text]-ideal to be stable is given.

A class of sub-almost distributive lattices in an associate almost distributive lattice through a filter

2019 ◽  
Vol 13 (07) ◽  
pp. 2050136
Author(s):  
S. Ramesh ◽  
Jogarao Gunda
Keyword(s):  
Boolean Algebra ◽  
Distributive Lattice ◽  
Distributive Lattices ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Algebraic Properties ◽  
Necessary And Sufficient

In this paper, we introduce a class of sub-almost distributive lattices in an associate almost distributive lattice through a filter. We obtain several algebraic properties on the class of sub-almost distributive lattices and prove that the above class forms a distributive lattice. We derive a necessary and sufficient condition that the class to become a Boolean algebra.

KERNEL IDEALS IN ALMOST DISTRIBUTIVE LATTICES

2012 ◽  
Vol 05 (02) ◽  
pp. 1250024
Author(s):  
M. Sambasiva Rao ◽  
G. C. Rao
Keyword(s):  
Distributive Lattice ◽  
Distributive Lattices ◽  
Prime Ideals ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Kernel Ideal ◽  
Minimal Prime ◽  
Necessary And Sufficient ◽  
Equivalent Conditions

The concepts of ⋆-congruences and kernel ideals are introduced in a pseudo-complemented almost distributive lattice (ADL). A necessary and sufficient condition for a congruence to become a ⋆-congruence is derived. Some equivalent conditions for every ideal of a pseudo-complemented ADL to become a kernel ideal are derived. Prime kernel ideals are characterized in terms of minimal prime ideals. Properties of kernel ideals are observed in Stone ADLs.

Multi-Fuzzy Complex Nilpotent Matrices

2016 ◽  
Vol 5 (4) ◽  
pp. 52-76 ◽  
Author(s):  
Asit Dey ◽  
Madhumangal Pal
Keyword(s):  
Distributive Lattice ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Complex Matrix ◽  
Fuzzy Matrix ◽  
Nilpotent Matrix ◽  
Nilpotent Matrices ◽  
Necessary And Sufficient

In this paper, the concept of multi-fuzzy matrix (MFM), multi-fuzzy complex matrix (MFCM), generalized multi-fuzzy complex matrix (GMFCM), generalized multi-fuzzy complex nilpotent matrix (GMFCNM) are introduced and have shown that the set of GMFCMs form a distributive lattice. Some properties and characterizations for GMFCNMs are established and in particular, a necessary and sufficient condition for an n × n GMFCNM to have the nilpotent index n is given. Finally, the reduction of GMFCNMs over a distributive lattice are given with some properties.

Dense elements characterization of quasi-complemented Almost Distributive Lattices

2014 ◽  
Vol 07 (04) ◽  
pp. 1450062
Author(s):  
G. C. Rao ◽  
G. Nanaji Rao ◽  
A. Lakshmana
Keyword(s):  
Boolean Algebra ◽  
Distributive Lattices ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Necessary And Sufficient

The properties of the set D of dense elements of an ADL are studied. The filter congruence θD generated by D in quasi-complemented ADLs is characterized. Quasi-complemented ADLs is characterized in terms of dense elements. A necessary and sufficient condition for a quasi-complemented ADLs to become a Boolean algebra is established.

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.

scholarly journals Lorentz Boosts and Wigner Rotations: Self-Adjoint Complexified Quaternions

Physics ◽  
2021 ◽  
Vol 3 (2) ◽  
pp. 352-366
Author(s):  
Thomas Berry ◽  
Matt Visser
Keyword(s):  
Point Of View ◽  
Sufficient Condition ◽  
Use Of Self ◽  
Necessary And Sufficient Condition ◽  
Wigner Rotation ◽  
Inertial Frames ◽  
Explicit Formulae ◽  
Specific Implementation ◽  
Necessary And Sufficient ◽  
Lorentz Boosts

In this paper, Lorentz boosts and Wigner rotations are considered from a (complexified) quaternionic point of view. It is demonstrated that, for a suitably defined self-adjoint complex quaternionic 4-velocity, pure Lorentz boosts can be phrased in terms of the quaternion square root of the relative 4-velocity connecting the two inertial frames. Straightforward computations then lead to quite explicit and relatively simple algebraic formulae for the composition of 4-velocities and the Wigner angle. The Wigner rotation is subsequently related to the generic non-associativity of the composition of three 4-velocities, and a necessary and sufficient condition is developed for the associativity to hold. Finally, the authors relate the composition of 4-velocities to a specific implementation of the Baker–Campbell–Hausdorff theorem. As compared to ordinary 4×4 Lorentz transformations, the use of self-adjoint complexified quaternions leads, from a computational view, to storage savings and more rapid computations, and from a pedagogical view to to relatively simple and explicit formulae.

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