scholarly journals Complete Cohomology for Extriangulated Categories

2021 ◽  
Vol 28 (04) ◽  
pp. 701-720
Author(s):  
Jiangsheng Hu ◽  
Dongdong Zhang ◽  
Tiwei Zhao ◽  
Panyue Zhou
Keyword(s):  
Projective Dimension ◽  
Proper Class ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Injective Dimension ◽  
General Technique ◽  
Gorenstein Algebra ◽  
Projective Resolutions ◽  
Necessary And Sufficient

Let [Formula: see text] be an extriangulated category with a proper class [Formula: see text] of [Formula: see text]-triangles. We study complete cohomology of objects in [Formula: see text] by applying [Formula: see text]-projective resolutions and [Formula: see text]-injective coresolutions constructed in [Formula: see text]. Vanishing of complete cohomology detects objects with finite [Formula: see text]-projective dimension and finite [Formula: see text]-injective dimension. As a consequence, we obtain some criteria for the validity of the Wakamatsu tilting conjecture and give a necessary and sufficient condition for a virtually Gorenstein algebra to be Gorenstein. Moreover, we give a general technique for computing complete cohomology of objects with finite [Formula: see text]-[Formula: see text]projective dimension. As an application, the relations between [Formula: see text]-projective dimension and [Formula: see text]-[Formula: see text]projective dimension for objects in [Formula: see text] are given.

On subprojectivity domains of g-semiartinian modules

2020 ◽  
pp. 2150119
Author(s):  
Yılmaz Durğun ◽  
Ayşe Çobankaya
Keyword(s):  
Homomorphic Image ◽  
Proper Class ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Necessary And Sufficient ◽  
The Relationship

The aim of this paper is to reveal the relationship between the proper class generated projectively by g-semiartinian modules and the subprojectivity domains of g-semiartinian modules. A module [Formula: see text] is called g-semiartinian if every nonzero homomorphic image of [Formula: see text] has a singular simple submodule. It is proven that every g-semiartinian right [Formula: see text]-module has an epic projective envelope if and only if [Formula: see text] is a right PS ring if and only if every subprojectivity domain of any g-semiartinian right [Formula: see text]-module is closed under submodules. A g-semiartinian module whose domain of subprojectivity as small as possible is called gsap-indigent. We investigated the structure of rings whose (simple, coatomic) g-semiartinian right modules are gsap-indigent or projective. Furthermore, over right PS rings, necessary and sufficient condition to be gsap-indigent module was determined.

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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