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Generalized Derivations of Prime Rings [PDF]
International Journal of Mathematics and Mathematical Sciences, 2007 Let R be an associative prime ring, U a Lie ideal such that u2∈U for all u∈U. An additive function F:R→R is called a generalized derivation if there exists a derivation d:R→R such that F(xy)=F(x)y+xd(y) holds for all x,y∈R. In this paper, we prove that
Huang Shuliang
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On Prime Rings with Derivations
AxiomsThis paper identifies all derivations associated with two well-known non-commutative prime rings and provides some remarks on one of these derivations, called the prime derivation.
Khalid H. Al-Shaalan
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∇-prime rings and their commutativity [PDF]
Journal of Taibah University for Science, 2023 Consider a ring with an (anti)-automorphism ∇ of finite order. The fundamental aim of this manuscript is to introduce the notions of ∇-(semi)prime ideal and ∇-(semi)prime ring as a generalization of the notions of (semi)prime ideal, [Formula: see text ...
Mohammad Aslam Siddeeque +1 more
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On generalized homoderivations of prime rings
Математичні Студії, 2023 Let $\mathscr{A}$ be a ring with its center $\mathscr{Z}(\mathscr{A}).$ An additive mapping $\xi\colon \mathscr{A}\to \mathscr{A}$ is called a homoderivation on $\mathscr{A}$ if $\forall\ a,b\in \mathscr{A}\colon\quad \xi(ab)=\xi(a)\xi(b)+\xi(a)b+a\xi(
N. Rehman +2 more
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Quotient rings satisfying some identities
Cubo, 2023 This paper investigates the commutativity of the quotient ring \(\mathcal{R}/P\), where \(\mathcal{R}\) is an associative ring with a prime ideal \(P\), and the possibility of forms of derivations satisfying certain algebraic identities on \(\mathcal{R}\)
Mohammadi El Hamdaoui, Abdelkarim Boua
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On the primeness of near-rings [PDF]
Arab Journal of Mathematical Sciences, 2020 In this paper, we study the different kinds of the primeness on the class of near-rings and we give new characterizations for them. For that purpose, we introduce new concepts called set-divisors, ideal-divisors, etc.
Khalid H. Al-Shaalan
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Homoderivations in Prime Rings
Journal of New Theory, 2023 The study consists of two parts. The first part shows that if $h_{1}(x)h_{2}(y)=h_{3}(x)h_{4}(y)$, for all $x,y\in R$, then $ h_{1}=h_{3}$ and $h_{2}=h_{4}$. Here, $h_{1},h_{2},h_{3},$ and $h_{4}$ are zero-power valued non-zero homoderivations of a prime
Neşet Aydın, Ayşe Engin
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The Source of Primeness of Rings
Journal of New Theory, 2022 In this study, we define a new concept, i.e., source of primeness of a ring $R$, as $P_{R} := \bigcap_{a\in R} S_{R}^{a}$ such that $S_{R}^{a}:=\{b\in R \mid aRb=(0)\}$. We then examine some basic properties of $P_{R}$ related to the ring’s idempotent elements, nilpotent elements, zero divisor elements, and identity elements.
Didem Yeşil +1 more
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ON COMMUTATIVITY OF PRIME NEAR RINGS [PDF]
Matrix Science Mathematic, 2021 In this paper, we prove commutativity of prime near rings by using the notion of β-derivations. Let M be a zero symmetric prime near ring. If there exist p ≥ 0, q ≥ 0 and a nonzero two sided β-derivation d on M, where β : M → M is a homomorphism, such ...
Abdul Rauf Khan +2 more
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On fuzzy quasi-prime ideals in near left almost rings [PDF]
Songklanakarin Journal of Science and Technology (SJST), 2019 In this investigation we studied fuzzy quasi-prime, weakly fuzzy quasi-prime, fuzzy completely prime and weakly fuzzy completely prime ideals in nLA-rings.
Pairote Yiarayong
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