scholarly journals Graded artin algebras, rational series, and bounds for homological dimensions

1987 ◽  
Vol 106 (2) ◽  
pp. 476-483 ◽  
Author(s):  
Dan Zacharia
Keyword(s):  
Rational Series ◽  
Homological Dimensions ◽  
Artin Algebras

scholarly journals Dominant and global dimension of blocks of quantised Schur algebras

2021 ◽  
Author(s):  
Ming Fang ◽  
Wei Hu ◽  
Steffen Koenig
Keyword(s):  
Hecke Algebras ◽  
Symmetric Groups ◽  
Global Dimension ◽  
Group Algebras ◽  
Dominant Dimension ◽  
Schur Algebras ◽  
Homological Dimensions ◽  
Weyl Duality

AbstractGroup algebras of symmetric groups and their Hecke algebras are in Schur-Weyl duality with classical and quantised Schur algebras, respectively. Two homological dimensions, the dominant dimension and the global dimension, of the indecomposable summands (blocks) of these Schur algebras S(n, r) and $$S_q(n,r)$$ S q ( n , r ) with $$n \geqslant r$$ n ⩾ r are determined explicitly, using a result on derived invariance in Fang, Hu and Koenig (J Reine Angew Math 770:59–85, 2021).

Stochastic Sensitivity Analysis of Structural Systems With Interval Uncertainties

2013 ◽  
Author(s):  
Giuseppe Muscolino ◽  
Roberta Santoro ◽  
Alba Sofi
Keyword(s):  
Sensitivity Analysis ◽  
Series Expansion ◽  
Neumann Series ◽  
Mean Value ◽  
Frame Structure ◽  
Young’S Moduli ◽  
Rational Series ◽  
Power Spectral ◽  
Stochastic Sensitivity Analysis ◽  
Neumann Series Expansion

Interval sensitivity analysis of linear discretized structures with uncertain-but-bounded parameters subjected to stationary multi-correlated Gaussian stochastic processes is addressed. The proposed procedure relies on the use of the so-called Interval Rational Series Expansion (IRSE), recently proposed by the authors as an alternative explicit expression of the Neumann series expansion for the inverse of a matrix with a small rank-r modification and properly extended to handle also interval matrices. The IRSE allows to derive approximate explicit expressions of the interval sensitivities of the mean-value vector and Power Spectral Density (PSD) function matrix of the interval stationary stochastic response. The effectiveness of the proposed method is demonstrated through numerical results pertaining to a seismically excited three-storey frame structure with interval Young’s moduli of some columns.

Homological Dimensions Relative to Special Subcategories

2021 ◽  
Vol 28 (01) ◽  
pp. 131-142
Author(s):  
Weiling Song ◽  
Tiwei Zhao ◽  
Zhaoyong Huang
Keyword(s):  
Abelian Category ◽  
Projective Dimension ◽  
Homological Dimensions ◽  
Category Of Modules ◽  
The Right

Let [Formula: see text] be an abelian category, [Formula: see text] an additive, full and self-orthogonal subcategory of [Formula: see text] closed under direct summands, [Formula: see text] the right Gorenstein subcategory of [Formula: see text] relative to [Formula: see text], and [Formula: see text] the left orthogonal class of [Formula: see text]. For an object [Formula: see text] in [Formula: see text], we prove that if [Formula: see text] is in the right 1-orthogonal class of [Formula: see text], then the [Formula: see text]-projective and [Formula: see text]-projective dimensions of [Formula: see text] are identical; if the [Formula: see text]-projective dimension of [Formula: see text] is finite, then the [Formula: see text]-projective and [Formula: see text]-projective dimensions of [Formula: see text] are identical. We also prove that the supremum of the [Formula: see text]-projective dimensions of objects with finite [Formula: see text]-projective dimension and that of the [Formula: see text]-projective dimensions of objects with finite [Formula: see text]-projective dimension coincide. Then we apply these results to the category of modules.

scholarly journals Projective resolutions over Artin algebras with zero relations

1985 ◽  
Vol 29 (1) ◽  
pp. 180-190 ◽  
Author(s):  
E. L. Green ◽  
D. Happel ◽  
D. Zacharia
Keyword(s):  
Artin Algebras ◽  
Projective Resolutions

scholarly journals Homological dimensions and regular rings

2009 ◽  
Vol 322 (10) ◽  
pp. 3451-3458 ◽  
Author(s):  
Alina Iacob ◽  
Srikanth B. Iyengar
Keyword(s):  
Homological Dimensions ◽  
Regular Rings

scholarly journals Gorenstein Projective Modules over Triangular Matrix Rings

2016 ◽  
Vol 23 (01) ◽  
pp. 97-104 ◽  
Author(s):  
H. Eshraghi ◽  
R. Hafezi ◽  
Sh. Salarian ◽  
Z. W. Li
Keyword(s):  
Triangular Matrix ◽  
Projective Modules ◽  
Matrix Rings ◽  
Matrix Algebras ◽  
Gorenstein Projective Modules ◽  
Artin Algebras ◽  
Acyclic Complexes ◽  
Matrix Extension

Let R and S be Artin algebras and Γ be their triangular matrix extension via a bimodule SMR. We study totally acyclic complexes of projective Γ-modules and obtain a complete description of Gorenstein projective Γ-modules. We then construct some examples of Cohen-Macaulay finite and virtually Gorenstein triangular matrix algebras.

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