Results 31 to 40 of about 28,236 (225)

Extensions of rational modules

International Journal of Mathematics and Mathematical Sciences, 2003
For a coalgebra C, the rational functor Rat (−):ℳC∗→ℳC∗ is a left exact preradical whose associated linear topology is the family ℱC, consisting of all closed and cofinite right ideals of C∗.
J. Cuadra
doaj   +1 more source

Some Characterizations of w-Noetherian Rings and SM Rings

Journal of Mathematics, 2022
In this paper, we characterize w-Noetherian rings and SM rings. More precisely, in terms of the u-operation on a commutative ring R, we prove that R is w-Noetherian if and only if the direct limit of rGV-torsion-free injective R-modules is injective and ...
De Chuan Zhou, Hwankoo Kim, Xiaolei Zhang, Jin Xie   +3 more
doaj   +1 more source

Geometric idealizers [PDF]

, 2008
Let X be a projective variety, $\sigma$ an automorphism of X, L a $\sigma$-ample invertible sheaf on X, and Z a closed subscheme of X. Inside the twisted homogeneous coordinate ring $B = B(X, L, \sigma)$, let I be the right ideal of sections vanishing at
Sierra, Susan J.
core   +2 more sources

Co-Cohen-Macaulay Modules and Local Cohomology

Journal of Mathematics, 2013
Let be a commutative Noetherian local ring and let be a finitely generated -module of dimension . Then the following statements hold: (a) if width for all with , then is co-Cohen-Macaulay of Noetherian dimension ; (b) if is an unmixed -module and ...
Hero Saremi, Amir Mafi
doaj   +1 more source

Noncommutative generalizations of theorems of Cohen and Kaplansky [PDF]

, 2011
This paper investigates situations where a property of a ring can be tested on a set of "prime right ideals." Generalizing theorems of Cohen and Kaplansky, we show that every right ideal of a ring is finitely generated (resp.
A Kertész, AV Jategaonkar, AV Jategaonkar, AW Goldie, AW Goldie, BL Osofsky, BV Zabavs’kiĭ, D Eisenbud, DV Huynh, EG Evans Jr, G Krause, I Kaplansky, IS Cohen, JA Beachy, JC McConnell, JC Robson, JC Robson, JJ Koker, K Koh, K Koh, KR Goodearl, KR Goodearl, Manuel L. Reyes, ML Reyes, PF Smith, PF Smith, PF Smith, PM Cohn, R Gordon, SA Amitsur, SM Bhatwadekar, TY Lam, TY Lam, TY Lam, TY Lam, TY Lam, TY Lam, VR Chandran, VR Chandran   +38 more
core   +2 more sources

On Nonnil-S-Noetherian Rings

Mathematics, 2020
Let R be a commutative ring with identity, and let S be a (not necessarily saturated) multiplicative subset of R. We define R to be a nonnil-S-Noetherian ring if each nonnil ideal of R is S-finite.
Min Jae Kwon, Jung Wook Lim
doaj   +1 more source

On nonnil-coherent modules and nonnil-Noetherian modules

Open Mathematics, 2022
In this article, we introduce two new classes of modules over a ϕ\phi -ring that generalize the classes of coherent modules and Noetherian modules. We next study the possible transfer of the properties of being nonnil-Noetherian rings, ϕ\phi -coherent ...
Haddaoui Younes El, Kim Hwankoo, Mahdou Najib   +2 more
doaj   +1 more source

Faithful Noetherian Modules [PDF]

Proceedings of the American Mathematical Society, 1973
The Eakin-Nagata theorem says that if T T is a commutative Noetherian ring which is finitely generated as a module over a subring R R , then R R is also Noetherian. This paper proves a generalization of this result.
openaire   +2 more sources

Examples of non-Noetherian domains inside power series rings [PDF]

, 2014
Let R* be an ideal-adic completion of a Noetherian integral domain R and let L be a subfield of the total quotient ring of R* such that L contains R. Let A denote the intersection of L with R*.
Heinzer, William, Rotthaus, Christel, Wiegand, Sylvia   +2 more
core   +3 more sources

A generalized version of the rings $C_K(X)$ and $C_\infty(X)$ - an enquery about when they become Noetherian

Applied General Topology, 2015
Suppose $F$ is a totally ordered field equipped with its order topology and $X$ a completely $F$-regular topological space. Suppose $\mathcal{P}$ is an ideal of closed sets in $X$ and $X$ is locally-$\mathcal{P}$.
Sudip Kumar Acharyya, Kshitish Chandra Chattopadhyay, Pritam Rooj   +2 more
doaj   +1 more source