Results 51 to 60 of about 179 (118)

On semiprime rings of bounded index [PDF]

Proceedings of the American Mathematical Society, 1982
A ring R R is of bounded index (of nilpotency) if there is an integer
openaire   +1 more source

Effects of Generalized Semiderivations on Algebraic Identities Involving Prime Ideals

Journal of Mathematics, Volume 2025, Issue 1, 2025.
In this article, instead of a generalized derivation, we will use the concept of a generalized semiderivation ∇ that satisfies various identities involving a prime ideal ß of an optional ring Λ to describe the behavior of a quotient ring Λ/ß. We will use this concept to generalize some well‐known results that studied the behavior of a ring Λ via a ...
Kholood Alnefaie, Pramita Mishra
wiley   +1 more source

A Pair of Generalized (α, α)‐Derivations With Identities Related to Prime Ideals

Journal of Mathematics, Volume 2025, Issue 1, 2025.
Let A be an arbitrary ring, α an automorphism of A, I a nonzero ideal of A, and ϒ a prime ideal of A satisfying the condition ϒ⊊αI. This research investigates the interplay between two generalized (α, α)‐derivations, Ω and G (associated with (α, α)‐derivations f and h, respectively), and the resulting characteristics of the quotient ring A/ϒ.
Ali Yahya Hummdi, Hafedh Alnoghashi, Radwan Mohammed Al-Omary, Abdelkarim Boua, Faranak Farshadifar   +4 more
wiley   +1 more source

Coweakly Uniserial Modules and Rings Whose (2‐Generated) Modules Are Coweakly Uniserial

Journal of Mathematics, Volume 2025, Issue 1, 2025.
A module is called weakly uniserial if for any two its submodules at least one of them is embedded in the other. This is a nontrivial generalization of uniserial modules and rings. Here, we introduce and study the dual of this concept. In fact, an R‐module M is called coweakly uniserial if for any submodules N, K of M, HomR(M/N, M/K) or HomR(M/K, M/N ...
M. M. Oladghobad, R. Beyranvand, Faranak Farshadifar   +2 more
wiley   +1 more source

Semiprime near-rings [PDF]

Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics, 1991
AbstractSome properties of v-semiprime (v = 0, 1, 2) near-rings are pointed out. In particular v semiprime near-rings which contain nil non-nilpotent ideals are studied.
S. De Stefano, S. Di Sieno
openaire   +3 more sources

On the generalization of torsion functor and P-semiprime modules over noncommutative rings [PDF]

Journal of Hyperstructures
Let R be an associative Noetherian unital noncommutative ring R. We introduce the functor PΓP over the category of R-modules and use it to characterize P-semiprime. P-semisecond R-modules also characterized by the functor PΛP.
Teklemichael Bihonegn, Tilahun Abebaw, Nega Arega   +2 more
doaj   +1 more source

A Unified Approach to Generalizing π‐Extending and π‐Baer Rings

Journal of Mathematics, Volume 2025, Issue 1, 2025.
This paper introduces and examines the right essentially π‐Baer ring property, which serves as a new extension of the π‐extending and π‐Baer ring conditions. The initial phase of the study involves the development of several foundational results. The subsequent phase of the study involves the exploration of the transfer of the right essentially π‐Baer ...
Yeliz Kara, Ali Jaballah
wiley   +1 more source

COMMUTING AND 2-COMMUTING DERIVATIONS OF SEMIPRIME RINGS

Journal of Kufa for Mathematics and Computer, 2012
The main purpose of this paper is to study and investigate some results concerning generalized derivation D on semiprime ring R, we obtain a derivation d is commuting  and 2-commuting on R.
Mehsin Jabel Atteya, Dalal Ibraheem Resan   +1 more
doaj   +1 more source

A Note on Skew Derivations and Antiautomorphisms of Prime Rings

Journal of Mathematics, Volume 2025, Issue 1, 2025.
In this article, we investigate the behavior of a prime ring which admits a skew derivation satisfying certain functional identities involving an antiautomorphism. We employ tools such as generalized identities and commutativity‐preserving maps to analyze these rings.
Faez A. Alqarni, Nadeem U. R. Rehman, Hafedh Alnoghashi, Junaid Nisar, Omar Al-Mallah, Ali Jaballah   +5 more
wiley   +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