Results 21 to 30 of about 708,128 (192)

A RESULT ON SEMI-ARTINIAN RINGS [PDF]

Proceedings of the Edinburgh Mathematical Society, 2003
AbstractIt was shown by Huynh and Rizvi that a ring $R$ is semisimple artinian if and only if every continuous right $R$-module is injective. However, a characterization of rings, over which every finitely generated continuous right module is injective, has been left open. In this note we give a partial solution for this question.
Dinh, Hai Quang, Smith, Patrick F.
openaire   +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

Rad-⊕-Supplemented Modules

Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica, 2013
In this paper we provide various properties of Rad-⊕-supplemented modules. In particular, we prove that a projective module M is Rad- ⊕-supplemented if and only if M is ⊕-supplemented, and then we show that a commutative ring R is an artinian serial ring
Türkmen Ergül
doaj   +1 more source

Pythagorean fuzzy Artinian and Noetherian ring [PDF]

Computational Algorithms and Numerical Dimensions
The Pythagorean fuzzy set is acknowledged for its proficiency in managing uncertainty across multifarious domains. In this investigation, we advance the Pythagorean fuzzy Artinian ring as an evolutionary progression from the conventional fuzzy ring ...
Meryem Fakhraoui, Idris Bakhadach, Sofyane Achik, Hamid Sadiki   +3 more
doaj   +1 more source

Equationally compact Artinian rings [PDF]

, 1971
By Noetherian (Artinian) ring
Haley, David K.
core   +1 more source

On rigid derivations in rings

Karpatsʹkì Matematičnì Publìkacìï, 2014
We prove that in a ring $R$ with an identity there exists an element $a\in R$ and a nonzero derivation $d\in Der R$ such that $ad(a)\neq 0$. A ring $R$ is said to be a $d$-rigid ring for some derivation $d \in Der R$ if  $d(a)=0$ or $ad(a)\neq 0$ for all
O.D. Artemovych, M.P. Lukashenko
doaj   +1 more source

PERFECTNESS OF THE ANNIHILATOR GRAPH OF ARTINIAN COMMUTATIVE RINGS [PDF]

Journal of Algebraic Systems, 2023
‎Let $R$ be a commutative ring and $Z(R)$ be the set of its zero-divisors‎.‎The annihilator graph of $R$‎, ‎denoted by $AG(R)$ is a simple undirected graph whose vertex‎‎set is $Z(R)^*$‎, ‎the set of all nonzero zero-divisors of $R$‎, ‎and two distinct ...
M. Adlifard, Sh. Payrovi
doaj   +1 more source

On formal local homology modules [PDF]

Journal of Hyperstructures, 2015
Throughout R is a commutative Noetherian ring and a an ideal of R. In this paper we study formal homology modules of Artinian R-modules. We obtain an expression of the formal homology in terms of a certain local homology module.
M.H. Bijan-Zadeh
doaj   +1 more source

Some results on top local cohomology modules with respect to a pair of ideals [PDF]

Mathematica Bohemica, 2020
Let $I$ and $J$ be ideals of a Noetherian local ring $(R,\mathfrak m)$ and let $M$ be a nonzero finitely generated $R$-module. We study the relation between the vanishing of $H_{I,J}^{\dim M}(M)$ and the comparison of certain ideal topologies.
Saeed Jahandoust, Reza Naghipour
doaj   +1 more source

Structure of rings with certain conditions on zero divisors

International Journal of Mathematics and Mathematical Sciences, 2006
Let R be a ring such that every zero divisor x is expressible as a sum of a nilpotent element and a potent element of R:x=a+b, where a is nilpotent, b is potent, and ab=ba. We call such a ring a D*-ring.
Hazar Abu-Khuzam, Adil Yaqub
doaj   +1 more source