Varieties of complexes of fixed rank

Firstly, we compare the bounded derived categories with respect to the pure-exact and the usual exact structures, and describe bounded derived category by pure-projective modules, under a fairly strong assumption on the ring. Then, we study Verdier quotient of bounded pure derived category modulo the bounded homotopy category of pure-projective modules, which is called a pure singularity category since we show that it reflects the finiteness of pure-global dimension of rings. Moreover, invariance of pure singularity in a recollement of bounded pure derived categories is studied.

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Relative Gorenstein Dimensions over Triangular Matrix Rings

Mathematics ◽

10.3390/math9212676 ◽

2021 ◽

Vol 9 (21) ◽

pp. 2676

Author(s):

Driss Bennis ◽

Rachid El Maaouy ◽

Juan Ramón García Rozas ◽

Luis Oyonarte

Keyword(s):

Matrix Ring ◽

Triangular Matrix ◽

Projective Dimension ◽

Global Dimension ◽

Projective Modules ◽

Matrix Rings ◽

Weakly Compatible ◽

Gorenstein Algebra ◽

Finite Projective Dimension ◽

Triangular Matrix Ring

Let A and B be rings, U a (B,A)-bimodule, and T=A0UB the triangular matrix ring. In this paper, several notions in relative Gorenstein algebra over a triangular matrix ring are investigated. We first study how to construct w-tilting (tilting, semidualizing) over T using the corresponding ones over A and B. We show that when U is relative (weakly) compatible, we are able to describe the structure of GC-projective modules over T. As an application, we study when a morphism in T-Mod is a special GCP(T)-precover and when the class GCP(T) is a special precovering class. In addition, we study the relative global dimension of T. In some cases, we show that it can be computed from the relative global dimensions of A and B. We end the paper with a counterexample to a result that characterizes when a T-module has a finite projective dimension.

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On the law of nullity

Mathematical Proceedings of the Cambridge Philosophical Society ◽

10.1017/s0305004100059430 ◽

1982 ◽

Vol 91 (3) ◽

pp. 357-374 ◽

Cited By ~ 3

Author(s):

P. M. Cohn ◽

A. H. Schofield

Keyword(s):

Global Dimension ◽

The Other ◽

Rank Function ◽

Projective Modules ◽

Natural Numbers ◽

Finitely Generated ◽

Skew Field ◽

Other Hand ◽

Semihereditary Rings

In chapter 7 of (2) conditions were given for a ring to be embeddable in a skew field; in particular, it was shown that any semifir has a universal field of fractions, over which all full matrices can be inverted. This was generalized in two different directions, by Bergman (in a letter to one of the authors in 1971) and by Dicks and Sontag(7). Dicks and Sontag characterized those rings having a field of fractions in which all full matrices are inverted; they showed that this is equivalent to Sylvester's law of nullity, and further showed that this forces the ring to have weak global dimension not exceeding 2 and all finitely generated projective modules to be free. Bergman on the other hand investigated weakly semihereditary rings having a rank function on projective modules which takes values in the natural numbers. He showed that there was a homomorphism from any such ring to a field of fractions in which every full map between finitely generated projective modules is inverted. Weakly semihereditary rings with a rank function to the natural numbers are the analogue of semifirs and so it is natural to look for a characterization of rings with a rank function on projective modules such that all full maps between projective modules become invertible in a suitable field of fractions. We shall find that, as before, this is the case if and only if Sylvester's law of nullity holds with respect to the rank function, for maps between projective modules. Further, the ring must have weak global dimension at most two. This is the content of Sections 2 and 3.

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DEVELOPMENT OF THE WORLD MARKET OF SERVICES IN TURBULENCE CONDITIONS AND CHANGES

International scientific journal Internauka ◽

10.25313/2520-2057-2020-18-6559 ◽

2017 ◽

Author(s):

Larysa Nosach ◽

◽

Victoria Morgun ◽

Keyword(s):

Economic Development ◽

International Trade ◽

Service Sector ◽

World Market ◽

Global Dimension ◽

Trade In Services ◽

Current State ◽

The World

The author's research of the current state and features of the development of the world market for services in conditions of turbulence of world processes was carried; the world leaders of the service sector in the global dimension and leaders of the most dynamic articles of service categories were identified; the share of world exports of services by countries by the level of their economic development was justified; weaknesses in the assessment of indicators of international trade in services were identified; the research is based on UNCTAD statistics.

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Projective modules and orbit space of unimodular rows over Discrete Hodge algebras over a non-Noetherian ring

Journal of Commutative Algebra ◽

10.1216/jca-2018-10-3-435 ◽

2018 ◽

Vol 10 (3) ◽

pp. 435-455

Author(s):

Md. Ali Zinna

Keyword(s):

Noetherian Ring ◽

Orbit Space ◽

Projective Modules

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Invariance of projective modules in $$\mathsf {Sup}$$ under self-duality

Algebra Universalis ◽

10.1007/s00012-020-00691-5 ◽

2021 ◽

Vol 82 (1) ◽

Author(s):

Javier Gutiérrez García ◽

Ulrich Höhle ◽

Tomasz Kubiak

Keyword(s):

Projective Modules ◽

Self Duality

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Subtitling Calligraphy

Journal of Chinese Film Studies ◽

10.1515/jcfs-2021-0004 ◽

2021 ◽

Vol 1 (1) ◽

pp. 115-133

Author(s):

Markus Nornes

Keyword(s):

East Asia ◽

Human Body ◽

Chinese Character ◽

Intimate Relationship ◽

Global Dimension ◽

Written Language ◽

Chinese Cinema ◽

Specific Difference ◽

Art Forms ◽

Sister Arts

Abstract This essay examines a regional, not global, dimension of Chinese cinema: the Chinese character in its brushed form. Calligraphy and cinema have an intimate relationship in East Asia. Indeed, the ubiquity of the brushed word in cinema is one element that actually ties works in Korean, Japanese and Sinophone Asia together as a regional cinema. At the same time, I will explore the very specific difference of Chinese filmmakers’ use of written language. On first glance, cinema and calligraphy would appear as radically different art forms. On second glance, they present themselves as sister arts. Both are art forms built from records of the human body moving in (an absent) time and space. The essay ends with a consideration of subtitling, upon which Chinese cinema’s global dimension is predicated. How does investigating this very problem lead us to rethinking the nature of the cinematic subtitle, which is very much alive―a truly movable type?

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On the Ehrhart Polynomial of Minimal Matroids

Discrete & Computational Geometry ◽

10.1007/s00454-021-00313-4 ◽

2021 ◽

Author(s):

Luis Ferroni

Keyword(s):

Ehrhart Polynomial ◽

Matroid Polytopes ◽

Connected Matroid ◽

Fixed Rank

AbstractWe provide a formula for the Ehrhart polynomial of the connected matroid of size n and rank k with the least number of bases, also known as a minimal matroid. We prove that their polytopes are Ehrhart positive and $$h^*$$ h ∗ -real-rooted (and hence unimodal). We prove that the operation of circuit-hyperplane relaxation relates minimal matroids and matroid polytopes subdivisions, and also preserves Ehrhart positivity. We state two conjectures: that indeed all matroids are $$h^*$$ h ∗ -real-rooted, and that the coefficients of the Ehrhart polynomial of a connected matroid of fixed rank and cardinality are bounded by those of the corresponding minimal matroid and the corresponding uniform matroid.

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‘A Most Select Gathering’. Mexican National Pilgrimages to Rome during the Papacy of Leo XIII

Religions ◽

10.3390/rel12070475 ◽

2021 ◽

Vol 12 (7) ◽

pp. 475

Author(s):

Francisco Javier Ramón Solans

Keyword(s):

Nineteenth Century ◽

National Identity ◽

Global Dimension ◽

National Identities ◽

Primary Sources ◽

Holy See

The objective of this article is to analyse Mexican national pilgrimages to Rome that took place during the pontificate of Leo XIII (1878–1903). These pilgrimages occurred in the context of a global Catholic mobilisation in support of the papacy, during the so-called Roman Question. This paper’s analysis of these pilgrimages draws from historiography about national pilgrimages, as well as studies on Catholic mobilisation in support of the pope in the second half of the nineteenth century. It is fundamentally based on primary sources of an official nature, such as reports and other printed documents produced on the occasion of the pilgrimage. The study’s primary conclusion is that national pilgrimages to Rome had a polysemic character since they brought together various religious and national identities. The pilgrimages contributed simultaneously to reinforcing the link between Catholicism and Mexican national identity and the global dimension of Catholicism and allegiance to the Holy See.

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The Corporate Governance of Environmental Sustainability: A Review and Proposal for More Integrated Research

Journal of Management ◽

10.1177/0149206321991212 ◽

2021 ◽

pp. 014920632199121

Author(s):

Ruth V. Aguilera ◽

J. Alberto Aragón-Correa ◽

Valentina Marano ◽

Peter A. Tashman

Keyword(s):

Corporate Governance ◽

Environmental Sustainability ◽

Boards Of Directors ◽

Global Dimension ◽

Top Management Teams ◽

Future Research ◽

Environmental Initiatives ◽

Integrative Framework ◽

Integrated Research ◽

Systematic Understanding

As corporations’ environmental impact comes under greater scrutiny by global financial, regulatory, and societal stakeholders, management scholars have increasingly focused on the role of corporate governance as a tool for driving environmental initiatives. Still, we lack a comprehensive and systematic understanding of this emergent body of inquiry and a holistic agenda for future research. To address this gap, our integrative framework relates the key corporate governance actors to environmental sustainability outcomes from the extant literature and highlights its main methodological approaches and theoretical arguments. Our framework provides a critical analysis of what we know and points to the knowledge gaps around owners, boards of directors, CEOs, top management teams, and employees as corporate governance actors. We then highlight limitations in the existing literature as significant opportunities for further research to resolve its ambiguous conceptualizations of environmental sustainability constructs, various methodological and theoretical challenges, incomplete engagement with the global dimension of environmental sustainability, and limited analysis of how corporate governance actors may interact to shape environmental sustainability outcomes. We conclude by proposing novel approaches for addressing these issues, which we believe could generate a better way forward on studying the corporate governance of environmental sustainability.

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