noetherian modules
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2017 ◽  
Vol 46 (2) ◽  
pp. 863-869 ◽  
Author(s):  
Zehra Bı̇lgı̇n ◽  
Manuel L. Reyes ◽  
Ünsal Tekı̇r

2015 ◽  
Vol 219 (10) ◽  
pp. 4510-4520 ◽  
Author(s):  
Nguyen Tu Cuong ◽  
Pham Hung Quy ◽  
Hoang Le Truong
Keyword(s):  

2014 ◽  
Vol 24 (02) ◽  
pp. 233-249
Author(s):  
Leonid A. Kurdachenko ◽  
Javier Otal ◽  
Igor Ya. Subbotin

In this paper, we study the structure of some Noetherian modules over group rings and deduce some statements regarding the structure of the groups involved. More precisely, we consider a module A over a group ring RG with the following property: A is a Noetherian RH-module for every subgroup H, which is not contained in the centralizer CG(A). If G is some generalized soluble group and R is a locally finite field or some Dedekind domain, we describe the structure of G/CG(A).


2013 ◽  
Vol 13 (02) ◽  
pp. 1350084
Author(s):  
NGUYEN THI HONG LOAN

Let (R, 𝔪) be a Noetherian local ring with dim R = d and M an R-module with dim M < d. We prove in this paper that the idealization R ⋉ M of M over R is a pseudo Buchsbaum ring if and only if so is R.


2011 ◽  
Vol 84 (3) ◽  
pp. 433-440
Author(s):  
A. HAGHANY ◽  
M. MAZROOEI ◽  
M. R. VEDADI

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.


2010 ◽  
Vol 52 (A) ◽  
pp. 19-32 ◽  
Author(s):  
TOMA ALBU

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.


2006 ◽  
Vol 98 (1) ◽  
pp. 12 ◽  
Author(s):  
G. Bilhan ◽  
P. F. Smith
Keyword(s):  

It is proved that, for any ring $R$, a right $R$-module $M$ has the property that, for every submodule $N$, either $N$ or $M/N$ is Noetherian if and only if $M$ contains submodules $K \supseteq L$ such that $M/K$ and $L$ are Noetherian and $K/L$ is almost Noetherian.


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