Results 61 to 70 of about 677,100 (167)

Generalized Derivations in Semiprime Gamma Rings [PDF]

International Journal of Mathematics and Mathematical Sciences, 2012
LetMbe a 2-torsion-free semiprimeΓ-ring satisfying the conditionaαbβc=aβbαcfor alla,b,c∈M,  α,β∈Γ, and letD:M→Mbe an additive mapping such thatD(xαx)=D(x)αx+xαd(x)for allx∈M,  α∈Γand for some derivationdofM. We prove thatDis a generalized derivation.
Kalyan Kumar Dey, Akhil Chandra Paul, Isamiddin S. Rakhimov   +2 more
openaire   +4 more sources

Fully noncentral Lie ideals and invariant additive subgroups in rings

Journal of the London Mathematical Society, Volume 111, Issue 3, March 2025.
Abstract We prove conditions ensuring that a Lie ideal or an invariant additive subgroup in a ring contains all additive commutators. A crucial assumption is that the subgroup is fully noncentral, that is, its image in every quotient is noncentral. For a unital algebra over a field of characteristic ≠2$\ne 2$ where every additive commutator is a sum of
Eusebio Gardella, Tsiu‐Kwen Lee, Hannes Thiel   +2 more
wiley   +1 more source

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

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

Prime Graphs of Polynomials and Power Series Over Noncommutative Rings

International Journal of Mathematics and Mathematical Sciences, Volume 2025, Issue 1, 2025.
The prime graph PG(R) of a ring R is a graph whose vertex set consists of all elements of R. Two elements x, y ∈ R are adjacent in the graph if and only if xRy = 0 or yRx = 0. An element a ∈ R is called a strong zero divisor in R if 〈a〉〈b〉 = 0 or 〈b〉〈a〉 = 0 for some nonzero element b ∈ R. The set of all strong zero divisors is denoted by S(R).
Walaa Obaidallah Alqarafi, Wafaa Mohammed Fakieh, Alaa Abdullah Altassan, Shikha Binwal   +3 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

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

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 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

On Graded Semiprime Submodules

, 2012
Let G be an arbitrary group with identity e and let R be a G-graded ring. In this paper we define graded semiprime submodules of a graded R-moduleM and we give a number of results concerning such submodules.
Farkhonde Farzalipour, Peyman Ghiasvand
core   +1 more source