Results 41 to 50 of about 443,027 (142)

Direct decompositions of artinian modules related to formations of groups [PDF]

, 2003
We survey direct decompositions of artinian modules over group rings into two summands where all the chief factors of the first are X–central and all the chief factors of the other is X–eccentric, where X is a certain formation of finite ...
Kurdachenko, L. A., Otal, J.
core   +2 more sources

Subrings of I-rings and S-rings

International Journal of Mathematics and Mathematical Sciences, 1997
Let R be a non-commutative associative ring with unity 1≠0, a left R-module is said to satisfy property (I) (resp. (S)) if every injective (resp. surjective) endomorphism of M is an automorphism of M.
Mamadou Sanghare
doaj   +1 more source

Cosupport of artinian modules

, 2021
Let $(R,\mathfrak{m})$ be a commutative local noetherian ring. For an artinian $R$-module $M$, we show the equality $$\mathrm{cosupp}_RM=\mathrm{Cosupp}_RM$$ using the semi-discrete linearly compactness of $R$-module $\mathrm{Hom}_R(R_\mathfrak{p},M)$ where $\mathfrak{p}$ is a prime ideal of $R$.
openaire   +2 more sources

Torsion pairs via the Ziegler spectrum

Proceedings of the London Mathematical Society, Volume 133, Issue 2, August 2026.
Abstract We establish a bijection between torsion pairs in the category of finite‐dimensional modules over a finite‐dimensional algebra A$A$ and pairs (Z,I)$(\mathcal {Z},\mathcal {I})$ formed by a closed rigid set Z$\mathcal {Z}$ in the Ziegler spectrum of A$A$ and a set I$\mathcal {I}$ of indecomposable injective A$A$‐modules. This is as an extension
Lidia Angeleri Hügel, Rosanna Laking, Francesco Sentieri   +2 more
wiley   +1 more source

The small condition for modules with Noetherian dimension [PDF]

Journal of Mahani Mathematical Research
A module $M$ with Noetherian dimension is said to satisfy the small condition, if for any small submodule $S$ of $M$ the Noetherian dimension of $S$ is strictly less than the Noetherian dimension of $M$. For an Artinian  module $M$, this is equivalent to
Nasrin Shirali, Hooriya Kavoosi Ghafi, Sayed Malek Javdannezhad   +2 more
doaj   +1 more source

From points to complexes: A concept of unexpectedness for simplicial complexes

Journal of the London Mathematical Society, Volume 114, Issue 1, July 2026.
Abstract In 2018, Cook, Harbourne, Migliore, and Nagel introduced the concept of unexpected hypersurfaces, which connects the study of Lefschetz properties of Artinian algebras defined by powers of linear forms to a family of interpolation problems.
Thiago Holleben
wiley   +1 more source

A Note on Artinianess of Certain Generalized [PDF]

Journal of Sciences, Islamic Republic of Iran, 2008
Let ?: R0?R be a ring homomorphism and suppose that a and a0, respectively, are ideals of R and R0 such that is an Artinian ring. Let M and N be two finitely generated R-modules and suppose that (R0,m0) is a local ring. In this note we prove that the R-
doaj  

The Cantor-Schröder-Bernstein Theorem in some categories of modules

Revista Integración
The Cantor-Schröder-Bernstein theorem has been studied in several categories throughout mathematics. In this article, we prove that this theorem holds in some relevant categories of modules, such as noetherian, and artinian, and prove that some strong ...
Diego Andrés Peralta Reyes, Héctor Edonis Pinedo Tapia   +1 more
doaj   +1 more source

A classification of Prüfer domains of integer‐valued polynomials on algebras

Bulletin of the London Mathematical Society, Volume 58, Issue 4, April 2026.
Abstract Let D$D$ be an integrally closed domain with quotient field K$K$ and A$A$ a torsion‐free D$D$‐algebra that is finitely generated as a D$D$‐module and such that A∩K=D$A\cap K=D$. We give a complete classification of those D$D$ and A$A$ for which the ring IntK(A)={f∈K[X]∣f(A)⊆A}$\textnormal {Int}_K(A)=\lbrace f\in K[X] \mid f(A)\subseteq A ...
Giulio Peruginelli, Nicholas J. Werner
wiley   +1 more source

Krull-Remak-Schmidt fails for artinian modules over local rings

, 2001
Ringel CM. Krull-Remak-Schmidt fails for artinian modules over local rings. Algebras and Representation Theory. 2001;4(1):77-86.Let R be a ring. Any R-module M which is Artinian or Noetherian can be written as the direct sum of a finite number of ...
Ringel, Claus Michael
core   +1 more source