Krull dimension and global dimension of simple Ore-extensions

1971 ◽  
Vol 121 (4) ◽  
pp. 341-345 ◽  
Author(s):  
Robert Hart
Keyword(s):  
Global Dimension ◽  
Krull Dimension ◽  
Ore Extensions

Global dimension of rings with krull dimension

1992 ◽  
Vol 20 (10) ◽  
pp. 2863-2876 ◽  
Author(s):  
John J. Koker
Keyword(s):  
Global Dimension ◽  
Krull Dimension

scholarly journals Global dimensions of right coherent rings with left Krull dimension

1989 ◽  
Vol 39 (2) ◽  
pp. 215-223 ◽  
Author(s):  
Mark L. Teply
Keyword(s):  
Noetherian Ring ◽  
Global Dimension ◽  
Krull Dimension ◽  
Prime Ideals ◽  
Homological Dimension ◽  
Isomorphism Classes ◽  
Coherent Ring ◽  
Gabriel Dimension ◽  
Coherent Rings

The weak global dimension of a right coherent ring with left Krull dimension α ≥ 1 is found to be the supremum of the weak dimensions of the β-critical cyclic modules, where β < α. If, in addition, the mapping I → assl gives a bijection between isomorphism classes on injective left R-modules and prime ideals of R, then the weak global dimension of R is the supremum of the weak dimensions of the simple left R-modules. These results are used to compute the left homological dimension of a right coherent, left noetherian ring. Some analogues of our results are also given for rings with Gabriel dimension.

On Krull dimension of ore extensions

1996 ◽  
Vol 3 (3) ◽  
pp. 263-274
Author(s):  
E. Rtveliashvili
Keyword(s):  
Krull Dimension ◽  
Ore Extensions

A note on the global dimension of ore extensions

1969 ◽  
Vol 108 (4) ◽  
pp. 253-254 ◽  
Author(s):  
N. S. Gopala Krishnan
Keyword(s):  
Global Dimension ◽  
Ore Extensions

Some Constructions of Bi-Koszul Algebras

2013 ◽  
Vol 20 (01) ◽  
pp. 141-154
Author(s):  
Junru Si ◽  
Jiafeng Lü
Keyword(s):  
Global Dimension ◽  
Koszul Algebras ◽  
Natural Question ◽  
Graded Algebras ◽  
Regular Algebras ◽  
Ore Extensions

Bi-Koszul algebras, including two classes of non-Koszul Artin-Schelter regular algebras of global dimension 4, were a class of graded algebras with non-pure resolutions, introduced in [8]. There is a natural question: can we construct bi-Koszul algebras from algebras with pure resolutions? In this paper, we study this question in terms of normal extensions and Ore extensions. More precisely, we attempt to obtain bi-Koszul algebras from algebras with pure resolutions by these two kinds of extensions. Furthermore, some homological properties of bi-Koszul algebras obtained in such ways are discussed.

Cohen macaulay rings of global dimension two and krull dimension two

1994 ◽  
Vol 22 (9) ◽  
pp. 3297-3329 ◽  
Author(s):  
Yu A. Drozd ◽  
K.W. Roggenkamp
Keyword(s):  
Global Dimension ◽  
Krull Dimension
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