scholarly journals Descending chains of submodules and the Krull-dimension of noetherian modules

1973 ◽  
Vol 3 (4) ◽  
pp. 385-397 ◽  
Author(s):  
Günter Krause
Keyword(s):  
Krull Dimension ◽  
Noetherian Modules

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.

scholarly journals GOLDIE DIMENSION, DUAL KRULL DIMENSION AND SUBDIRECT IRREDUCIBILITY

2010 ◽  
Vol 52 (A) ◽  
pp. 19-32 ◽  
Author(s):  
TOMA ALBU
Keyword(s):  
Krull Dimension ◽  
Subdirectly Irreducible ◽  
Modular Lattices ◽  
Survey Paper ◽  
Goldie Dimension ◽  
Subdirect Irreducibility ◽  
Upper Continuous ◽  
Torsion Theories ◽  
Quotient Modules ◽  
Noetherian Modules

AbstractIn this survey paper we present some results relating the Goldie dimension, dual Krull dimension and subdirect irreducibility in modules, torsion theories, Grothendieck categories and lattices. Our interest in studying this topic is rooted in a nice module theoretical result of Carl Faith [Commun. Algebra27 (1999), 1807–1810], characterizing Noetherian modules M by means of the finiteness of the Goldie dimension of all its quotient modules and the ACC on its subdirectly irreducible submodules. Thus, we extend his result in a dual Krull dimension setting and consider its dualization, not only in modules, but also in upper continuous modular lattices, with applications to torsion theories and Grothendieck categories.

Lengths of submodule chains versus Krull dimension in non-Noetherian modules

1986 ◽  
Vol 191 (4) ◽  
pp. 519-527 ◽  
Author(s):  
K. R. Goodearl ◽  
B. Zimmermann-Huisgen
Keyword(s):  
Krull Dimension ◽  
Noetherian Modules

scholarly journals Direct Sum Cancellation of Noetherian Modules

1998 ◽  
Vol 200 (1) ◽  
pp. 207-224 ◽  
Author(s):  
Gary Brookfield
Keyword(s):  
Direct Sum ◽  
Noetherian Modules

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
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