Results 71 to 80 of about 1,324,184 (168)

On Maps of Period 2 on Prime and Semiprime Rings

International Journal of Mathematics and Mathematical Sciences, 2014
A map f of the ring R into itself is of period 2 if f2x=x for all x∈R; involutions are much studied examples. We present some commutativity results for semiprime and prime rings with involution, and we study the existence of derivations and generalized ...
H. E. Bell, M. N. Daif
doaj   +1 more source

On a theorem of McCoy [PDF]

Mathematica Bohemica
We study McCoy's theorem to the skew Hurwitz series ring $({\rm HR}, \omega)$ for some different classes of rings such as: semiprime rings, APP rings and skew Hurwitz serieswise quasi-Armendariz rings.
Rajendra Kumar Sharma, Amit B. Singh
doaj   +1 more source

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   +3 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

Semiprime RΓ-Submodules of Multiplication RΓ-Modules

Iraqi Journal of Science, 2020
Let R be a Γ-ring and G be an RΓ-module. A proper RΓ-submodule S of G is said to be semiprime RΓ-submodule if for any ideal I of a Γ-ring R and for any RΓ-submodule A of G such that or which implies that .
Ali Abd Alhussein Zyarah, N. Al-Mothafar
semanticscholar   +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

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

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

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