Global Dimension of Differential Operator Rings. IV – Simple Modules

1989 ◽  
Vol 1 (1) ◽  
Author(s):  
Kenneth R. Goodearl
Keyword(s):  
Differential Operator ◽  
Global Dimension ◽  
Simple Modules

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

Global Dimensions of Subidealizer Rings

1995 ◽  
Vol 2 (4) ◽  
pp. 419-424
Author(s):  
John Koker
Keyword(s):  
Global Dimension ◽  
Simple Modules ◽  
Proper Subclass

Abstract Recently, there have been many results which show that the global dimension of certain rings can be computed using a proper subclass of the cyclic modules, e.g., the simple modules. In this paper we view calculating global dimensions in this fashion as a property of a ring and show that this is a property which transfers to the ring's idealizer and subidealizer ring.

scholarly journals The homological dimensions of simple modules

1993 ◽  
Vol 48 (2) ◽  
pp. 265-274 ◽  
Author(s):  
Nanqing Ding ◽  
Jianlong Chen
Keyword(s):  
Global Dimension ◽  
Simple Modules ◽  
Homological Dimensions ◽  
Coherent Ring ◽  
The Right

We prove that (a) if R is a commutative coherent ring, the weak global dimension of R equals the supremum of the flat (or (FP–)injective) dimensions of the simple R-modules; (b) if R is right semi-artinian, the weak (respectively, the right) global dimension of R equals the supremum of the flat (respectively, projective) dimensions of the simple right R-modules; (c) if R is right semi-artinian and right coherent, the weak global dimension of R equals the supremum of the FP-injective dimensions of the simple right R-modules.

scholarly journals PBW deformations of Artin–Schelter regular algebras

2016 ◽  
Vol 15 (04) ◽  
pp. 1650064 ◽  
Author(s):  
Jason Gaddis
Keyword(s):  
Tensor Products ◽  
Global Dimension ◽  
One Dimensional ◽  
Simple Modules ◽  
Regular Algebras ◽  
Skew Polynomial ◽  
Polynomial Extensions

We consider properties and extensions of PBW deformations of Artin–Schelter regular algebras. PBW deformations in global dimension two are classified and the geometry associated to the homogenizations of these algebras is exploited to prove that all simple modules are one-dimensional in the non-PI case. It is shown that this property is maintained under tensor products and certain skew polynomial extensions.

scholarly journals (Weak) Gorenstein Global Dimension of Semiartinian Rings

ISRN Algebra ◽  
2011 ◽  
Vol 2011 ◽  
pp. 1-6 ◽  
Author(s):  
Mohammed Tamekkante ◽  
Mohamed Chhiti
Keyword(s):  
Commutative Ring ◽  
Global Dimension ◽  
Simple Modules ◽  
Gorenstein Flat

We prove that if is a semiartinian commutative ring, the Gorenstein global dimension of equals the supremum of the Gorenstein projective and injective dimensions of simple -modules, and the weak Gorenstein global dimension of equals the supremum of the Gorenstein flat dimensions of simple -modules.

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