scholarly journals Acceptable Morita Contexts for Semigroups

ISRN Algebra ◽  
2012 ◽  
Vol 2012 ◽  
pp. 1-5 ◽  
Author(s):  
Valdis Laan
Keyword(s):  
Short Note ◽  
Morita Equivalence ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Morita Context ◽  
Necessary And Sufficient

This short note deals with Morita equivalence of (arbitrary) semigroups. We give a necessary and sufficient condition for a Morita context containing two semigroups S and T to induce an equivalence between the category of closed right S-acts and the category of closed right T-acts.

scholarly journals Bakry-Émery Conditions on Almost Smooth Metric Measure Spaces

2018 ◽  
Vol 6 (1) ◽  
pp. 129-145 ◽  
Author(s):  
Shouhei Honda
Keyword(s):  
Riemannian Manifolds ◽  
Short Note ◽  
Sufficient Condition ◽  
Metric Measure Spaces ◽  
Necessary And Sufficient Condition ◽  
Local Dimension ◽  
Base Points ◽  
Smooth Metric Measure Spaces ◽  
Measure Spaces ◽  
Necessary And Sufficient

Abstract In this short note, we give a sufficient condition for almost smooth compact metric measure spaces to satisfy the Bakry-Émery condition BE(K, N). The sufficient condition is satisfied for the glued space of any two (not necessary same dimensional) closed pointed Riemannian manifolds at their base points. This tells us that the BE condition is strictly weaker than the RCD condition even in this setting, and that the local dimension is not constant even if the space satisfies the BE condition with the coincidence between the induced distance by the Cheeger energy and the original distance. In particular, the glued space gives a first example with a Ricci bound from below in the Bakry-Émery sense, whose local dimension is not constant. We also give a necessary and sufficient condition for such spaces to be RCD(K, N) spaces.

An Elementary Result on Exponential Measure Spaces

1972 ◽  
Vol 15 (2) ◽  
pp. 277-278
Author(s):  
C. Y. Shen
Keyword(s):  
Measure Space ◽  
Measure Zero ◽  
Measure Theory ◽  
Short Note ◽  
Measurable Subset ◽  
Sufficient Condition ◽  
Product Spaces ◽  
Necessary And Sufficient Condition ◽  
Measure Spaces ◽  
Necessary And Sufficient

A simple but useful result in the measure theory for product spaces can be stated as follows:Theorem A. A necessary and sufficient condition that a measurable subset E of X×Y has measure zero is that almost every X-section (or almost every Y-section) has measure zero (see [1, §36]).We will show, in this short note, that a similar result also holds for the exponential of measure spaces. Before proceeding any further, we describe briefly here the exponential construction of a measure space.

scholarly journals A Characterization of the Intuitionistic Propositional Logic

1970 ◽  
Vol 37 ◽  
pp. 131-136
Author(s):  
Nobol Muti
Keyword(s):  
Propositional Logic ◽  
Short Note ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Intuitionistic Propositional Logic ◽  
Necessary And Sufficient

In this short note, is shown a necessary and sufficient condition for a logic to be an intermediate propositional logic in Umezawa’s sense (see the reference), under such an assumption that any logic in consideration (as a subclass of LK-provable propositions) contains at least the axioms of the positive propositional logic LPS (Curry’s LA) as its axioms and is closed with respect to the rules of detachment and substitution.

The p.p. property of trivial extensions

2015 ◽  
Vol 14 (08) ◽  
pp. 1550124 ◽  
Author(s):  
M. Tamer Koşan
Keyword(s):  
Trivial Extension ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Morita Context ◽  
Necessary And Sufficient

In this note, a necessary and sufficient condition for a trivial extension to be a left p.p.-ring is obtained. As an application, we determine when a trivial Morita context is a left p.p.-ring, and a result of Xue [On p.p. rings, Kobe J. Math. 7 (1990) 77–80] characterizing triangular p.p.-rings follows immediately.

scholarly journals ENHANCED FINITE TRIANGULATED CATEGORIES

2020 ◽  
pp. 1-43
Author(s):  
Fernando Muro
Keyword(s):  
Morita Equivalence ◽  
Triangulated Category ◽  
Triangulated Categories ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Necessary And Sufficient

We give a necessary and sufficient condition for the existence of an enhancement of a finite triangulated category. Moreover, we show that enhancements are unique when they exist, up to Morita equivalence.

scholarly journals Projectivity and duality in a Morita context

1993 ◽  
Vol 47 (1) ◽  
pp. 95-100 ◽  
Author(s):  
Zhou Zhengping
Keyword(s):  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Morita Context ◽  
Closed Submodule ◽  
Left And Right ◽  
Necessary And Sufficient ◽  
Special Case

The concepts of closed submodule, left and right annihilators are generalised and a necessary and sufficient condition on any Morita context is given so that the duality and projectivity between these sets exist. As a special case, we get Hutchinson's necessary and sufficient condition under a weaker hypothesis on the context.

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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