scholarly journals HOLONOMIC FILTERED MODULES IN THE CATEGORY OF MICRO-STRUCTURE SHEAVES

2020 ◽  
Vol 27 (4) ◽  
pp. 337-342
Author(s):  
ABD EL AZIZ A. RADWAN ◽  
SALAH EL DIN S. HUSSEIN
Keyword(s):  
Regularity Condition ◽  
Global Dimension ◽  
Noetherian Rings ◽  
Regularity Conditions ◽  
Graded Rings ◽  
General Study ◽  
Micro Structure ◽  
Sheaf Theory ◽  
Structure Sheaf ◽  
Filtered Modules

Since the late sixties, Various Auslander regularity conditions have been widely investigated in both commutative and non-commutative cases, [6]. J. E. Bjork studied the Auslander regularity on graded rings and positively filtered Noetherian Noetherian rings, [7]. In [7] the notion of a holonomic module over positively filtered rings has been introduced. Recently, Huishi, in his Ph. D. Thesis [12], investigate Auslander regularity condition and holonomity of graded and filtered modules over Zariski filtered rings. In this work, using the micro-structure sheaf techniques we characterize a generalized Holonomic sheaf theory. We introduce a general study of Auslander regularity on the micro-structure sheaves. We calculate the global dimension of modules over the micro- structure sheaves O . The main results are contained in Theorem (2.4), Theorem (3.6) and Theorem (3.7).

scholarly journals When Are Graded Rings Graded S-Noetherian Rings

Mathematics ◽  
2020 ◽  
Vol 8 (9) ◽  
pp. 1532
Author(s):  
Dong Kyu Kim ◽  
Jung Wook Lim
Keyword(s):  
Noetherian Ring ◽  
Semigroup Ring ◽  
Noetherian Rings ◽  
Homogeneous Ideal ◽  
Commutative Monoid ◽  
Graded Rings ◽  
Graded Ring ◽  
Special Case

Let Γ be a commutative monoid, R=⨁α∈ΓRα a Γ-graded ring and S a multiplicative subset of R0. We define R to be a graded S-Noetherian ring if every homogeneous ideal of R is S-finite. In this paper, we characterize when the ring R is a graded S-Noetherian ring. As a special case, we also determine when the semigroup ring is a graded S-Noetherian ring. Finally, we give an example of a graded S-Noetherian ring which is not an S-Noetherian ring.

Bounded Derived Categories of Infinite Quivers: Grothendieck Duality, Reflection Functor

2015 ◽  
Vol 67 (1) ◽  
pp. 28-54 ◽  
Author(s):  
Javad Asadollahi ◽  
Rasool Hafezi ◽  
Razieh Vahed
Keyword(s):  
Noetherian Ring ◽  
Global Dimension ◽  
Derived Categories ◽  
Noetherian Rings ◽  
Commutative Noetherian Ring ◽  
Finite Global Dimension

AbstractWe study bounded derived categories of the category of representations of infinite quivers over a ring R. In case R is a commutative noetherian ring with a dualising complex, we investigate an equivalence similar to Grothendieck duality for these categories, while a notion of dualising complex does not apply to them. The quivers we consider are left (resp. right) rooted quivers that are either noetherian or their opposite are noetherian. We also consider reflection functor and generalize a result of Happel to noetherian rings of finite global dimension, instead of fields.

scholarly journals On the Logarithmic Regularity Conditions for the Variable Exponent Hardy Type Inequality

2014 ◽  
Vol 2014 ◽  
pp. 1-5
Author(s):  
Aziz Harman ◽  
Mustafa Özgür Keleş
Keyword(s):  
Hardy Inequality ◽  
Variable Exponent ◽  
Regularity Condition ◽  
Type Inequality ◽  
Regularity Conditions ◽  
Hardy Type Inequality ◽  
Hardy Type

We discuss a logarithmic regularity condition in a neighborhood of the origin and infinity on the exponent functions qx≥px and βx for the variable exponent Hardy inequality xβ·-1∫0xftdtLp·0,l≤Cxβ·fLp·0,l to hold.

A structure sheaf on noetherian rings

1994 ◽  
Vol 22 (9) ◽  
pp. 3511-3530
Author(s):  
J.L. Bueso ◽  
P. Jara ◽  
L. Merino
Keyword(s):  
Noetherian Rings ◽  
Structure Sheaf

scholarly journals Noetherian Rings of Finite Global Dimension

1982 ◽  
Vol s3-44 (2) ◽  
pp. 349-371 ◽  
Author(s):  
K. A. Brown ◽  
C. R. Hajarnavis ◽  
A. B. Maceacharn
Keyword(s):  
Global Dimension ◽  
Noetherian Rings ◽  
Finite Global Dimension

scholarly journals Some properties of non-commutative regular graded rings

1992 ◽  
Vol 34 (3) ◽  
pp. 277-300 ◽  
Author(s):  
Thierry Levasseur
Keyword(s):  
Noetherian Ring ◽  
Global Dimension ◽  
Supplementary Condition ◽  
Graded Rings ◽  
Finitely Generated ◽  
Injective Dimension ◽  
Commutative Case ◽  
Finite Global Dimension ◽  
Image Position ◽  
Dimension One

Let A be a noetherian ring. When A is commutative (of finite Krull dimension), A is said to be Gorenstein if its injective dimension is finite. If A has finite global dimension, one says that A is regular. If A is arbitrary, these hypotheses are not sufficient to obtain similar results to those of the commutative case. To remedy this problem, M. Auslander has introduced a supplementary condition. Before stating it, we recall that the grade of a finitely generated (left or right) module is defined by

scholarly journals Weaker Regularity Conditions and Sparse Recovery in High-Dimensional Regression

2014 ◽  
Vol 2014 ◽  
pp. 1-7
Author(s):  
Shiqing Wang ◽  
Yan Shi ◽  
Limin Su
Keyword(s):  
Linear Regression ◽  
Regularity Condition ◽  
Sparse Recovery ◽  
High Dimensional ◽  
Regularity Conditions ◽  
Dantzig Selector ◽  
High Dimensional Regression ◽  
Prediction Risk ◽  
Eigenvalue Condition ◽  
Lasso Estimator

Regularity conditions play a pivotal role for sparse recovery in high-dimensional regression. In this paper, we present a weaker regularity condition and further discuss the relationships with other regularity conditions, such as restricted eigenvalue condition. We study the behavior of our new condition for design matrices with independent random columns uniformly drawn on the unit sphere. Moreover, the present paper shows that, under a sparsity scenario, the Lasso estimator and Dantzig selector exhibit similar behavior. Based on both methods, we derive, in parallel, more precise bounds for the estimation loss and the prediction risk in the linear regression model when the number of variables can be much larger than the sample size.

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