scholarly journals AUSLANDER GENERATORS AND HOMOLOGICAL CONJECTURES

2013 ◽  
Vol 56 (3) ◽  
pp. 503-506 ◽  
Author(s):  
JIAQUN WEI
Keyword(s):  
Artin Algebra ◽  
Representation Dimension ◽  
Homological Conjectures

AbstractLet A be an artin algebra with representation dimension not more than 3. Assuming that AV is an Auslander generator and M ∈ addAV, we show that both findim(EndAM) and findim(EndAM)op are finite, and consequently the Gorenstein symmetry conjecture, the Wakamatsu-tilting conjecture and the generalized Nakayama conjecture hold for EndAM.

Gorenstein global dimension and Hopf algebroid actions

2016 ◽  
Vol 15 (05) ◽  
pp. 1650090
Author(s):  
Yong Wang ◽  
Fang Li
Keyword(s):  
Triangular Matrix ◽  
Global Dimension ◽  
Smash Product ◽  
Artin Algebra ◽  
Representation Dimension ◽  
Hopf Algebroid ◽  
Hopf Algebroids ◽  
The Stability ◽  
Gorenstein Injective ◽  
The Relationship

Let [Formula: see text] be a Hopf algebroid and [Formula: see text] a left [Formula: see text]-module algebra. In this paper, we mainly present the duality theorem for the smash product [Formula: see text], and making use of integral theory for Hopf algebroids, we investigate the stability of Gorenstein injective pre-envelopes and Gorenstein projective precovers between the category of [Formula: see text]-modules and the category of [Formula: see text]-modules. Moreover, we establish the relationship between Gorenstein global dimension of [Formula: see text] and that of [Formula: see text], and prove that [Formula: see text] has finite representation type, resp. is selfinjective, resp. is CM-finite [Formula: see text]-Gorenstein, if and only if [Formula: see text] has the same property under suitable conditions. As an application, we investigate the representation dimension of the lower triangular matrix Artin algebra [Formula: see text].

scholarly journals Excellent Extensions and Homological Conjectures

2018 ◽  
Vol 25 (04) ◽  
pp. 619-626
Author(s):  
Yingying Zhang
Keyword(s):  
Finite Group ◽  
Group Algebra ◽  
Finitistic Dimension ◽  
Artin Algebra ◽  
A Finite Group ◽  
Excellent Extension ◽  
Special Case ◽  
Skew Group Algebra ◽  
Dimension Conjecture ◽  
Homological Conjectures

In this paper, we introduce the notion of excellent extensions of rings. Let Γ be an excellent extension of an Artin algebra Λ, we prove that Λ satisfies the Gorenstein symmetry conjecture (resp., finitistic dimension conjecture, Auslander–Gorenstein conjecture, Nakayama conjecture) if and only if so does Γ. As a special case of excellent extensions, when G is a finite group whose order is invertible in Λ acting on Λ and Λ is G-stable, we prove that if the skew group algebra ΛG satisfies strong Nakayama conjecture (resp., generalized Nakayama conjecture), then so does Λ.

scholarly journals Maximal representation dimension of finitep-groups

2011 ◽  
pp. ---
Author(s):  
Shane Cernele ◽  
Masoud Kamgarpour ◽  
Zinovy Reichstein
Keyword(s):  
Representation Dimension ◽  
Maximal Representation

The Structure of Stable Components

1991 ◽  
Vol 43 (3) ◽  
pp. 652-672 ◽  
Author(s):  
Yingbo Zhang ◽  
T. Lang
Keyword(s):  
Artin Algebra ◽  
Valued Quiver ◽  
Cyclic Path

Let A be an artin algebra. Let ( be a component of the stable Auslander- Reiten quiver of A. If is periodic, then the structure of G is known. Here, we are going to consider the case when is non-periodic: we will show that is isomorphic to Z with a valued quiver. In particular, there is no cyclic path in .

Diversity recognition and minority representation in Central and Southeast Europe: a comparative analysis

2014 ◽  
Vol 42 (3) ◽  
pp. 426-448 ◽  
Author(s):  
István Gergőo Székely ◽  
István Horváth
Keyword(s):  
Comparative Analysis ◽  
Political Representation ◽  
Strong Relationship ◽  
Legal Analysis ◽  
Southeast Europe ◽  
Minority Representation ◽  
Representation Dimension ◽  
General Attitude ◽  
External Pressures ◽  
Ethnocultural Diversity

The need to handle ethnocultural diversity and the external pressures of Euro-Atlantic integration have led to the development of complex minority rights regimes in Central and Southeast European states. The aim of this paper is to perform a comparative analysis of the political representation dimension of these regimes, and to investigate how the regulations in this domain are related to the more general attitude of states toward diversity recognition and registration. For this purpose, we classify the states according to a series of variables concerning the manner in which ethnocultural diversity is recognized and portrayed, as well as the regulations concerning the representation of minorities, and identify patterns of their incidence. The formal-legal analysis of the constitutions, minority protection laws and of the electoral legislation of the included countries reveals a clear connection between the general attitude of the state toward diversity and the incidence of autonomies, and a less unequivocal, yet strong relationship in the case of minority representation in the national polity.

scholarly journals On the Auslander–Reiten quiver of a P1-hereditary artin algebra

2000 ◽  
Vol 151 (1) ◽  
pp. 11-29 ◽  
Author(s):  
Lidia Angeleri Hügel ◽  
Flávio U. Coelho
Keyword(s):  
Artin Algebra ◽  
Hereditary Artin Algebra
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