Results 31 to 40 of about 68 (65)
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
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On rings satisfying [(𝑎,𝑏,𝑐),𝑑]=0
, 1971 A simple nonassociative ring, in which the associators commute with all elements, is under mild additional assumptions either associative or commutative.
Armin Thedy
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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
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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
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 +2 more
wiley +1 more source
On dependent elements in rings
, 2004 Let R be an associative ring. An element ▫$ain R$▫ is said to be dependent on a mapping ▫$F:Rto R$▫ in case ▫$F(x)a=ax$▫ holds for all ▫$xin R$▫. In this paper, elements dependent on certain mappings on prime and semiprime rings are investigated.
Vukman, Joso +3 more
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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
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, 2004 In a recent paper we have extended the classical Herstein's theorem on Jordan derivations on prime rings to Jordan superderivations on prime associative superalgebras.
Fošner, Maja +2 more
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Algunas observaciones sobre la propiedad fusible de las extensiones polinomiales no conmutativas
, 2020 In this work, we focus on three objectives: first, we investigate fusible property on skew PBW extensions, recognizing conditions that guarantee the property for this family of algebras.
Higuera Rincón, Sebastián David
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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 +5 more
wiley +1 more source