scholarly journals STABLE TORSION THEORIES AND THE INJECTIVE HULLS OF SIMPLE MODULES

2014 ◽  
Vol 16 (16) ◽  
pp. 89-89 ◽  
Author(s):  
Can Hatipoğlu
Keyword(s):  
Simple Modules ◽  
Torsion Theories ◽  
Injective Hulls

scholarly journals INJECTIVE MODULES OVER DOWN-UP ALGEBRAS

2010 ◽  
Vol 52 (A) ◽  
pp. 53-59 ◽  
Author(s):  
PAULA A. A. B. CARVALHO ◽  
CHRISTIAN LOMP ◽  
DILEK PUSAT-YILMAZ
Keyword(s):  
Roots Of Unity ◽  
Finiteness Conditions ◽  
Simple Modules ◽  
Injective Modules ◽  
Injective Hulls

AbstractThe purpose of this paper is to study finiteness conditions on injective hulls of simple modules over Noetherian down-up algebras. We will show that the Noetherian down-up algebras A(α, β, γ) which are fully bounded are precisely those which are module-finite over a central subalgebra. We show that injective hulls of simple A(α, β, γ)-modules are locally Artinian provided the roots of X2 − αX − β are distinct roots of unity or both equal to 1.

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

scholarly journals Injective hulls of semi-simple modules over regular rings

1969 ◽  
Vol 31 (1) ◽  
pp. 247-255 ◽  
Author(s):  
Awadhesh Tiwary
Keyword(s):  
Simple Modules ◽  
Injective Hulls ◽  
Regular Rings

scholarly journals Splitting torsion theories over commutative rings

1975 ◽  
Vol 13 (3) ◽  
pp. 457-464 ◽  
Author(s):  
John D. Fuelberth ◽  
James Kuzmanovich ◽  
Thomas S. Shores
Keyword(s):  
Finite Number ◽  
Commutative Rings ◽  
Torsion Theory ◽  
Simple Modules ◽  
Torsion Theories ◽  
Theoretic Characterization

The purpose of this paper is to completely characterize splitting torsion theories over commutative rings. In particular, if (T, F) is a torsion theory for which T(R) = 0, then (T, F) is a splitting theory if and only if T contains only a finite number of nonisomorphic simple modules and every module in T is semisimple injective. In addition, an ideal theoretic characterization of splitting torsion theories is given, of which one consequence is that splitting torsion theories are TTF; furthermore, if R is also noetherian, then such torsion theories are centrally splitting. The known theorems concerning the splitting of the Goldie and simple torsion theories (for commutative rings) are derived from our theorem.

scholarly journals On injective hulls of simple modules

2000 ◽  
Vol 225 (1) ◽  
pp. 299-308 ◽  
Author(s):  
Y. Hirano
Keyword(s):  
Simple Modules ◽  
Injective Hulls

Prestressed Concrete Tests Compared With Torsion Theories

PCI Journal ◽  
1985 ◽  
Vol 30 (5) ◽  
pp. 96-127 ◽  
Author(s):  
Arthur E. McMullen ◽  
Wael M. EI-Degwy
Keyword(s):  
Prestressed Concrete ◽  
Torsion Theories
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