Results 71 to 80 of about 186 (173)

When Is a Simple Ring Noetherian?

Journal of Algebra, 1996
A module is called a \(CS\)-module if every submodule is essential in a direct summand. It is proved that a simple ring \(R\) is right Noetherian provided every cyclic singular right \(R\)-module is \(CS\). In addition, a simple ring \(R\) is right hereditary right Noetherian provided every proper cyclic right \(R\)-module is quasi-injective.
Van Huynh, Dinh, Jain, S.K., López-Permouth, S.R.   +2 more
openaire   +1 more source

Classes of modules closed under projective covers

Open Mathematics
In this work, we study some classes of modules closed under submodules, quotients, and projective covers, even if the left projective cover of an arbitrary left module not always exists. We obtain a characterization of artinian principal ideal rings when
Cejudo-Castilla César, García-Ramírez Ángel Raúl, Montalvo Ivan Fernando Vilchis   +2 more
doaj   +1 more source

Embedding Noetherian Rings in Artinian Rings

Journal of Algebra, 2001
A well-known theorem of \textit{A. H. Schofield} [``Representation of rings over skew fields'', Lond. Math. Soc. Lect. Note Ser. 92, CUP, Cambridge (1985; Zbl 0571.16001)] asserts that an algebra \(A\) over a field can be embedded in a right Artinian ring if and only if there is a faithful Sylvester rank function on finitely presented \(A\)-modules. By
openaire   +1 more source

Constructions over localizations of rings

Le Matematiche, 1987
In this paper we construct a category of effective noetherian rings in which linear equations can be “solved”. This category is closed with respect to some important constructions like trascendental extensions, quotientations, finite products and ...
Alessandro Logar
doaj  

A Note on Weakly Semiprime Ideals and Their Relationship to Prime Radical in Noncommutative Rings

Journal of Mathematics
In this paper, we introduce the concept of weakly semiprime ideals and weakly n-systems in noncommutative rings. We establish the equivalence between an ideal P being a weakly semiprime ideal and R−P being a weakly n-system.
Alaa Abouhalaka
doaj   +1 more source

Topological Noetherianity of polynomial functors II: base rings with Noetherian spectrum. [PDF]

Math Ann, 2023
Bik A, Danelon A, Draisma J.
europepmc   +1 more source

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

Filtered Products of Copies of Injective Modules

Axioms
We study the transfer of injectivity to filtered products of copies of an injective module. This leads to the introduction of a generalized Noetherian condition, the so-called (ℵ,M)-Noetherian rings. We prove that M is F-injective for every filter F with
Driss Bennis, Juan Ramón García Rozas, Maroua Mbarki, Luis Oyonarte   +3 more
doaj   +1 more source

On the arithmetic of stable domains. [PDF]

Commun Algebra, 2021
Bashir A, Geroldinger A, Reinhart A.
europepmc   +1 more source

Pure subrings of Du Bois singularities are Du Bois singularities

Forum of Mathematics, Sigma
Let $R \to S$ be a cyclically pure map of Noetherian $\mathbb {Q}$ -algebras. In this paper, we show that if S has Du Bois singularities, then R has Du Bois singularities. Our result is new even when $R \to S$ is faithfully flat.
Charles Godfrey, Takumi Murayama
doaj   +1 more source