Results 31 to 40 of about 708,128 (192)

Topologically left artinian rings

Journal of Algebra, 1985
In this paper are considered linearly topologized rings with identity all whose factor-modules at open left ideals are artinian (TA-rings). In the characterization of TA-rings an important role is played by a minimal cogenerator \({}_ RV\) of the class of \(R\)-torsion left \(R\)-modules. Some results about structure and features of the module \({}_ RV\
MENINI, Claudia, A. ORSATTI
openaire   +2 more sources

δ-Small Submodules and δ-Supplemented Modules

International Journal of Mathematics and Mathematical Sciences, 2007
Let R be a ring and M a right R-module. It is shown that (1) δ(M) is Noetherian if and only if M satisfies ACC on δ-small submodules; (2) δ(M) is Artinian if and only if M satisfies DCC on δ-small submodules; (3) M is Artinian if and only if M is an ...
Yongduo Wang
doaj   +1 more source

Modules with Artinian prime factors

, 1980
An R-module M has Artinian prime factors if M / P M M/PM is an Artinian module for each prime ideal P of R.
Efraim P. Armendariz
core   +1 more source

The Relationships between Relatively Cancellation Modules and Certain Types of Modules

مجلة بغداد للعلوم, 2011
Let R be a commutative ring with identity and M be unitary (left) R-module. The principal aim of this paper is to study the relationships between relatively cancellation module and multiplication modules, pure submodules and Noetherian (Artinian) modules.
Baghdad Science Journal
doaj   +1 more source

SIMPLE AND SEMI-SIMPLE ARTINIAN RINGS [PDF]

, 2017
The main purpose of this paper is to examine the road towards the structure of simple and semi-simple Artinian rings. We refer to these structure theorems as the Wedderburn-Artin theorems. On this journey, we will discuss R-modules, the Jacobson radical,
Velasco, Ulyses
core   +5 more sources

Characterization of rings with planar, toroidal or projective planar prime ideal sum graphs

AKCE International Journal of Graphs and Combinatorics
Let R be a commutative ring with unity. The prime ideal sum graph [Formula: see text] of the ring R is the simple undirected graph whose vertex set is the set of all nonzero proper ideals of R and two distinct vertices I and J are adjacent if and only if
Praveen Mathil, Barkha Baloda, Jitender Kumar, A. Somasundaram   +3 more
doaj   +1 more source

On the mapping xy→(xy)n in an associative ring

International Journal of Mathematics and Mathematical Sciences, 2004
We consider the following condition (*) on an associative ring R:(*). There exists a function f from R into R such that f is a group homomorphism of (R,+), f is injective on R2, and f(xy)=(xy)n(x,y) for some positive integer n(x,y)>1. Commutativity and
Scott J. Beslin, Awad Iskander
doaj   +1 more source

A note on CS-semisimple ring

Tạp chí Khoa học, 2023
In this paper, we introduce condition (∗) for modules and show that every CS-semisimple ring having condition (∗) is a QF ring.
Le Van An, Nguyen Thi Hai Anh
doaj   +1 more source

On the State Approach Representations of Convolutional Codes over Rings of Modular Integers

Mathematics, 2021
In this study, we prove the existence of minimal first-order representations for convolutional codes with the predictable degree property over principal ideal artinian rings.
Ángel Luis Muñoz Castañeda, Noemí DeCastro-García, Miguel V. Carriegos   +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