The decomposition of minimax modules over hyperfinite groups

1993 ◽  
Vol 61 (4) ◽  
pp. 340-343 ◽  
Author(s):  
Z. Y. Duan ◽  
M. J. Tomkinson
Keyword(s):  
Minimax Modules

Minimax modules, local homology and local cohomology

2015 ◽  
Vol 26 (12) ◽  
pp. 1550102 ◽  
Author(s):  
Tran Tuan Nam
Keyword(s):  
Local Cohomology ◽  
Local Homology ◽  
Local Cohomology Modules ◽  
Minimax Modules ◽  
Equivalent Properties ◽  
Cohomology Modules

We show some results about local homology modules and local cohomology modules concerning Grothendieck’s conjecture and Huneke’s question. We also show some equivalent properties of [Formula: see text]-separated modules and of minimax local homology modules. By duality, we get some properties of Grothendieck’s local cohomology modules.

On the generalized local cohomology of minimax modules

2016 ◽  
Vol 15 (08) ◽  
pp. 1650147 ◽  
Author(s):  
H. Roshan-Shekalgourabi ◽  
D. Hassanzadeh-Lelekaami
Keyword(s):  
Noetherian Ring ◽  
Local Cohomology ◽  
Betti Numbers ◽  
Commutative Noetherian Ring ◽  
Minimax Modules ◽  
Bass Numbers

Let [Formula: see text] be a commutative Noetherian ring with identity and [Formula: see text] be an ideal of [Formula: see text]. Assume that [Formula: see text] is a finite [Formula: see text]-module and [Formula: see text] and [Formula: see text] are minimax [Formula: see text]-modules such that [Formula: see text]. In this paper, among other things, we show that [Formula: see text] is minimax for all [Formula: see text] and [Formula: see text] when one of the following conditions holds: [Formula: see text](i) [Formula: see text]; [Formula: see text] (ii) [Formula: see text]; or (iii) [Formula: see text]. As a consequence, we obtain that the Bass numbers and Betti numbers of [Formula: see text] are finite for all [Formula: see text] when one of the above conditions holds.

On Minimax and Related Modules

1992 ◽  
Vol 44 (1) ◽  
pp. 154-166 ◽  
Author(s):  
Peter Rudlof
Keyword(s):  
Homomorphic Image ◽  
Finite Codimension ◽  
Noetherian Rings ◽  
Finitely Generated ◽  
Maximal Submodule ◽  
Minimax Modules ◽  
Minimax Module ◽  
Generalized Classes

AbstractA module M is called a minimax module, if it has a finitely generated submodule U such that M/U is Artinian. This paper investigates minimax modules and some generalized classes over commutative Noetherian rings. One of our main results is: M is minimax iff every decomposition of a homomorphic image of M is finite.From this we deduce that:- All couniform modules are minimax.- All modules of finite codimension are minimax.- Essential covers of minimax modules are minimax. With the aid of these corollaries we completely determine the structure of couniform modules and modules of finite codimension.We then examine the following variants of the minimax property:- replace U “ finitely generated” by U “ coatomic” (i.e. every proper submodule of U is contained in a maximal submodule);- replace M/U “ Artinian” by M/U “ semi-Artinian” (i.e. every proper submodule of M/U contains a minimal submodule).

scholarly journals Some results on the local cohomology of minimax modules

2014 ◽  
Vol 64 (2) ◽  
pp. 327-333 ◽  
Author(s):  
Ahmad Abbasi ◽  
Hajar Roshan-Shekalgourabi ◽  
Dawood Hassanzadeh-Lelekaami
Keyword(s):  
Local Cohomology ◽  
Minimax Modules
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