scholarly journals On cyclic essential extensions of simple modules over differential operator rings

2019 ◽  
Vol 47 (9) ◽  
pp. 3629-3648
Author(s):  
Alveri Sant’Ana ◽  
Robson Vinciguerra
Keyword(s):  
Differential Operator ◽  
Simple Modules ◽  
Essential Extensions

scholarly journals Injective Hulls of Simple Modules over Differential Operator Rings

2015 ◽  
Vol 43 (10) ◽  
pp. 4221-4230 ◽  
Author(s):  
Paula A. A. B. Carvalho ◽  
Can Hatipoğlu ◽  
Christian Lomp
Keyword(s):  
Differential Operator ◽  
Simple Modules ◽  
Injective Hulls

A NOTE ON ESSENTIAL EXTENSIONS OF SEMI-SIMPLE MODULES

2008 ◽  
Vol 07 (02) ◽  
pp. 225-230 ◽  
Author(s):  
NOYAN ER
Keyword(s):  
Chain Condition ◽  
Direct Sums ◽  
Simple Modules ◽  
Essential Extensions ◽  
Ascending Chain Condition

In a series of recent papers, Beidar, Jain and Srivastava studied the question as to when a ring R with the property that essential extensions of semi-simple right R-modules are direct sums of quasi-injectives is right Noetherian. Beidar and Jain proved that it is, when R is commutative or right q.f.d. In this note we extend their results proving the following: A ring R with this property is right Noetherian iff for some n ∈ ℕ, R/socn(RR) has ascending chain condition on essential non-two-sided right ideals (in particular, when R/socn(RR) is right q.f.d. or commutative). Also shown is the following: A ring is a right Noetherian right V-ring iff modules with essential socle are quasi-continuous/quasi-injective.

scholarly journals MONOLITHIC MODULES OVER NOETHERIAN RINGS

2011 ◽  
Vol 53 (3) ◽  
pp. 683-692 ◽  
Author(s):  
PAULA A. A. B. CARVALHO ◽  
IAN M. MUSSON
Keyword(s):  
Weyl Algebra ◽  
Noetherian Rings ◽  
Quantum Plane ◽  
Finiteness Conditions ◽  
Glasgow Math ◽  
Simple Modules ◽  
Injective Modules ◽  
Essential Extensions

AbstractWe study finiteness conditions on essential extensions of simple modules over the quantum plane, the quantised Weyl algebra and Noetherian down-up algebras. The results achieved improve the ones obtained by Carvalho et al. (Carvalho et al., Injective modules over down-up algebras, Glasgow Math. J. 52A (2010), 53–59) for down-up algebras.

scholarly journals Simple modules and their essential extensions for skew polynomial rings

2018 ◽  
Vol 291 (3-4) ◽  
pp. 877-903
Author(s):  
Ken Brown ◽  
Paula A. A. B. Carvalho ◽  
Jerzy Matczuk
Keyword(s):  
Polynomial Rings ◽  
Simple Modules ◽  
Skew Polynomial Rings ◽  
Skew Polynomial ◽  
Essential Extensions

Sturm-Liouville Problem for Stationary Differential Operator with Nonlocal Two-Point Boundary Conditions

2006 ◽  
Vol 11 (1) ◽  
pp. 47-78 ◽  
Author(s):  
S. Pečiulytė ◽  
A. Štikonas
Keyword(s):  
Boundary Condition ◽  
Differential Operator ◽  
Boundary Conditions ◽  
Nonlocal Boundary Condition ◽  
Nonlocal Boundary ◽  
Liouville Problem ◽  
Complex Case ◽  
Qualitative Behavior ◽  
Point Boundary ◽  
Sturm Liouville

The Sturm-Liouville problem with various types of two-point boundary conditions is considered in this paper. In the first part of the paper, we investigate the Sturm-Liouville problem in three cases of nonlocal two-point boundary conditions. We prove general properties of the eigenfunctions and eigenvalues for such a problem in the complex case. In the second part, we investigate the case of real eigenvalues. It is analyzed how the spectrum of these problems depends on the boundary condition parameters. Qualitative behavior of all eigenvalues subject to the nonlocal boundary condition parameters is described.

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