Results 51 to 60 of about 852 (157)
Additivity and Central Behavior of CE‐Generalized Homoderivations in Associative Rings
Journal of Mathematics, Volume 2026, Issue 1, 2026.This study examines the commutativity of a ring R endowed with a special class of mappings termed centrally extended generalized homoderivations. These mappings serve as an extension of several existing concepts, including homoderivations, generalized homoderivations, and left centralizers.
Hicham Saber +6 more
wiley +1 more source
Journal of Mathematics, Volume 2026, Issue 1, 2026.In this study, we investigate the behavior of semiprime ideals that satisfy certain algebraic identities using multiplicative (generalized) derivations. In addition, examples are provided to show that the limits imposed on the hypotheses of the different theorems are not superfluous.
Amal S. Alali +5 more
wiley +1 more source
Derivations of differentially semiprime rings
, 2019 Earlier D. A. Jordan, C. R. Jordan and D. S. Passman have investigated the properties of Lie rings Der [Formula: see text] of derivations in a commutative differentially prime rings [Formula: see text].
Orest D. Artemovych +3 more
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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 +2 more
wiley +1 more source
Jordan triple (α,β)-higher ∗-derivations on semiprime rings
Demonstratio Mathematica, 2023 In this article, we define the following: Let N0{{\mathbb{N}}}_{0} be the set of all nonnegative integers and D=(di)i∈N0D={\left({d}_{i})}_{i\in {{\mathbb{N}}}_{0}} a family of additive mappings of a ∗\ast -ring RR such that d0=idR{d}_{0}=i{d}_{R}. DD is
Ezzat O. H.
doaj +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 +3 more
wiley +1 more source
Orthogonal Semiderivations and Symmetric Bi-semiderivations in Semiprime Rings
Cumhuriyet Science Journal, 2022 In this paper, orthogonality for symmetric bi-semiderivations is defined and some results are obtained when two symmetric bi-semiderivations are orthogonal.
Damla Yılmaz
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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 +4 more
wiley +1 more source
A subdirect decomposition of semiprime rings and its application to maximal quotient rings
, 1974 Levy [2] has examined semiprime rings which are irredundant subdirect products of prime rings. In this note we look at the role of inessential prime ideals and see how every semiprime ring is a subdirect product of (i) a semiprime ring which is an ...
Louis Halle Rowen
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