scholarly journals Cluster categories for algebras of global dimension 2 and quivers with potential

2009 ◽  
Vol 59 (6) ◽  
pp. 2525-2590 ◽  
Author(s):  
Claire Amiot
Keyword(s):  
Global Dimension ◽  
Cluster Categories ◽  
Dimension 2 ◽  
Quivers With Potential

On the Weak Global Dimension of Pseudovaluation Domains

1978 ◽  
Vol 21 (2) ◽  
pp. 159-164 ◽  
Author(s):  
David E. Dobbs
Keyword(s):  
Integral Domain ◽  
Global Dimension ◽  
Valuation Domain ◽  
Valuation Domains ◽  
Dimension 2 ◽  
The Ideal

In [7], Hedstrom and Houston introduce a type of quasilocal integral domain, therein dubbed a pseudo-valuation domain (for short, a PVD), which possesses many of the ideal-theoretic properties of valuation domains. For the reader′s convenience and reference purposes, Proposition 2.1 lists some of the ideal-theoretic characterizations of PVD′s given in [7]. As the terminology suggests, any valuation domain is a PVD. Since valuation domains may be characterized as the quasilocal domains of weak global dimension at most 1, a homological study of PVD's seems appropriate. This note initiates such a study by establishing (see Theorem 2.3) that the only possible weak global dimensions of a PVD are 0, 1, 2 and ∞. One upshot (Corollary 3.4) is that a coherent PVD cannot have weak global dimension 2: hence, none of the domains of weak global dimension 2 which appear in [10, Section 5.5] can be a PVD.

QF - 1 Rings of Global Dimension ≦ 2

1973 ◽  
Vol 25 (2) ◽  
pp. 345-352
Author(s):  
Claus Michael Ringel
Keyword(s):  
Global Dimension ◽  
The Other ◽  
Frobenius Rings ◽  
Other Hand ◽  
Dimension 2 ◽  
Left And Right

R. M. Thrall [10] introduced QF — 1, QF — 2 and QF — 3 rings as generalizations of quasi-Frobenius rings. (For definitions, see section 1. It should be noted that all rings considered are assumed to be left and right artinian.) He proved that QF — 2 rings are QF — 3 and asked whether all QF — 1 rings are QF — 2, or, at least, QF — 3. In [9] we have shown that QF — 1 rings are very similar to QF — 3 rings. On the other hand, K. Morita [6] gave two examples of QF — 1 rings, one of them not QF — 2 and therefore not QF — 3, the other one QF — 3, but not QF — 2.

Generalized hereditary Noetherian prime rings

2018 ◽  
Vol 17 (08) ◽  
pp. 1850153 ◽  
Author(s):  
E. Akalan ◽  
H. Marubayashi ◽  
A. Ueda
Keyword(s):  
Global Dimension ◽  
Polynomial Rings ◽  
Prime Rings ◽  
Dimension 2 ◽  
Left And Right

The polynomial rings over hereditary Noetherian prime rings have global dimension 2 and any two-sided ideal which is either left [Formula: see text]-ideal or right [Formula: see text]-ideal is left and right projective. By using the latter property, we define the concept of generalized hereditary Noetherian prime rings (G-HNP rings). We study the structure of projective ideals in G-HNP rings and some overrings of G-HNP rings. As it is shown in the examples, the class of G-HNP rings ranges from rings with global dimension 2 to rings with infinite global dimension and Noetherian prime rings with global dimension 2 are not necessarily G-HNP rings.

Remarks on Op and Towber Rings

1970 ◽  
Vol 22 (6) ◽  
pp. 1109-1117 ◽  
Author(s):  
David Lissner ◽  
Anthony Geramita
Keyword(s):  
Noetherian Ring ◽  
Global Dimension ◽  
Finitely Generated ◽  
Outer Product ◽  
Dimension 2

In this paper all rings considered have identity and are commutative, and all modules are finitely generated. We shall make liberal use of the definitions and notation established in [6; 7].Towber observed in [9] that a local Outer Product ring (OP-ring) must have v-dimension ≦ 2, and so a local OP-ring is either regular of global dimension ≦ 2 or it has infinite global dimension. Since the global dimension of a noetherian ring is the supremum of the global dimensions of its localizations, we immediately obtain the following result.THEOREM 1.1. The global dimension of a noetherian OP-ring is either∞ or ≦ 2.

Derived invariants for surface cut algebras of global dimension 2 II: the punctured case

2020 ◽  
Vol 49 (1) ◽  
pp. 114-150
Author(s):  
Claire Amiot ◽  
Daniel Labardini-Fragoso ◽  
Pierre-Guy Plamondon
Keyword(s):  
Global Dimension ◽  
Dimension 2

scholarly journals Quadratic algebras with few relations

1997 ◽  
Vol 39 (3) ◽  
pp. 323-332
Author(s):  
James J. Zhang
Keyword(s):  
Vector Space ◽  
Global Dimension ◽  
Tensor Algebra ◽  
Dimensional Vector ◽  
High Term ◽  
Quadratic Algebras ◽  
Dimensional Vector Space ◽  
Finite Dimensional Vector Space ◽  
Finite Dimensional ◽  
Dimension 2

Throughout V will be a finite dimensional vector space over a field k and T(V) will denote the tensor algebra over V. For simplicity the symbol ⊗ will be omitted in the writing of the elements of T(V). Let be a basis of V ordered by Xi<Xi+1 for all i. Then we order the non-commutative monomials and 1 ≤ is ≤ n for s = 1,…, l} lexicographically from the left. D. Anick [1, p. 652] defines the high term of an element b in T(V) to be the highest monomial appearing in b. As a consequence of [1,3.2], if the set of the high terms of homogeneous relations is combinatorically free in the sense of no overlap ambiguities, then the connected algebra has global dimension 2. The purpose of this note is to prove this result and more for quadratic algebras under other hypotheses on the relations.

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

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.

scholarly journals Subtitling Calligraphy

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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