Krull dimension and artin algebras

1986 ◽  
pp. 135-155 ◽  
Author(s):  
Werner Geigle
Keyword(s):  
Krull Dimension ◽  
Artin Algebras

scholarly journals BOUNDED AND FULLY BOUNDED MODULES

2011 ◽  
Vol 84 (3) ◽  
pp. 433-440
Author(s):  
A. HAGHANY ◽  
M. MAZROOEI ◽  
M. R. VEDADI
Keyword(s):  
Krull Dimension ◽  
Finitely Generated ◽  
Morita Invariant ◽  
Prime Submodule ◽  
Invariant Properties ◽  
Noetherian Modules

AbstractGeneralizing the concept of right bounded rings, a module MR is called bounded if annR(M/N)≤eRR for all N≤eMR. The module MR is called fully bounded if (M/P) is bounded as a module over R/annR(M/P) for any ℒ2-prime submodule P◃MR. Boundedness and right boundedness are Morita invariant properties. Rings with all modules (fully) bounded are characterized, and it is proved that a ring R is right Artinian if and only if RR has Krull dimension, all R-modules are fully bounded and ideals of R are finitely generated as right ideals. For certain fully bounded ℒ2-Noetherian modules MR, it is shown that the Krull dimension of MR is at most equal to the classical Krull dimension of R when both dimensions exist.

Krull dimension of permutation modules

1993 ◽  
Vol 21 (2) ◽  
pp. 705-710
Author(s):  
Robert L. Snider
Keyword(s):  
Krull Dimension

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 Projective resolutions over Artin algebras with zero relations

1985 ◽  
Vol 29 (1) ◽  
pp. 180-190 ◽  
Author(s):  
E. L. Green ◽  
D. Happel ◽  
D. Zacharia
Keyword(s):  
Artin Algebras ◽  
Projective Resolutions

scholarly journals Gorenstein Projective Modules over Triangular Matrix Rings

2016 ◽  
Vol 23 (01) ◽  
pp. 97-104 ◽  
Author(s):  
H. Eshraghi ◽  
R. Hafezi ◽  
Sh. Salarian ◽  
Z. W. Li
Keyword(s):  
Triangular Matrix ◽  
Projective Modules ◽  
Matrix Rings ◽  
Matrix Algebras ◽  
Gorenstein Projective Modules ◽  
Artin Algebras ◽  
Acyclic Complexes ◽  
Matrix Extension

Let R and S be Artin algebras and Γ be their triangular matrix extension via a bimodule SMR. We study totally acyclic complexes of projective Γ-modules and obtain a complete description of Gorenstein projective Γ-modules. We then construct some examples of Cohen-Macaulay finite and virtually Gorenstein triangular matrix algebras.

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