Results 1 to 10 of about 186 (173)

HOMOLOGICAL DIMENSION IN NOETHERIAN RINGS. [PDF]

Proc Natl Acad Sci U S A, 1956
Introduction. Throughout this paper it is assumed that all rings are commutative, noetherian rings with unit element and all modules are unitary. The major purpose of this paper is to extend to arbitrary noetherian rings the homological invariants which were introduced in [2] for local rings.
Auslander M, Buchsbaum DA.
europepmc   +6 more sources

About j{\mathscr{j}}-Noetherian rings

Open Mathematics
Let RR be a commutative ring with identity and j{\mathscr{j}} an ideal of RR. An ideal II of RR is said to be a j{\mathscr{j}}-ideal if I⊈jI\hspace{0.33em} \nsubseteq \hspace{0.33em}{\mathscr{j}}.
Najib Mahdou
exaly   +2 more sources

A COUNTEREXAMPLE IN NOETHERIAN RINGS. [PDF]

Proc Natl Acad Sci U S A, 1965
Herstein IN.
europepmc   +5 more sources

AN EXAMPLE IN NOETHERIAN RINGS. [PDF]

Proc Natl Acad Sci U S A, 1965
Small LW.
europepmc   +4 more sources

Endo-Noetherian Skew Generalized Power Series Rings [PDF]

Assiut University Journal of Multidisciplinary Scientific Research, 2023
Endo-Noetherian modules were introduced by A. Kaidi and E. Sanchez] as a generalization of Noetherian modules. A left Ɍ-module M which satisfies the ascending chain condition for endomorphic kernels is said to be endo-Noetherian.
Ramy Abdel-Khaleq, Refaat Salem, Neamat Mohamed   +2 more
doaj   +1 more source

Integer-valued polynomials and binomially Noetherian rings

Zanco Journal of Pure and Applied Sciences, 2022
for each and i ≥ 0. The polynomial ring of integer-valued in rational polynomial is defined by Int ( an important example for binomial ring and is non-Noetherian ring. In this paper the algebraic structure of binomial rings has been studied by their
Shadman Kareem
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

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

Abnormalities in Noetherian Rings [PDF]

Proceedings of the American Mathematical Society, 1979
If P ⊆ Q ...
Arnold, J. T., Boisen, M. B. jun.
openaire   +1 more source

S-Noetherian rings, modules and their generalizations [PDF]

Surveys in Mathematics and its Applications, 2023
Let R be a commutative ring with identity, M an R-module and S ⊆ R a multiplicative set. Then M is called S-finite if there exist an s ∈ S and a finitely generated submodule N of M such that sM ⊆ N.
Tushar Singh, Ajim Uddin Ansari, Shiv Datt Kumar   +2 more
doaj