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JORDAN *-DERIVATIONS OF PRIME RINGS

Journal of Algebra and Its Applications, 2014
Let R be a prime ring, which is not commutative, with involution * and with Qms(R) the maximal symmetric ring of quotients of R. An additive map δ : R → R is called a Jordan *-derivation if δ(x2) = δ(x)x* + xδ(x) for all x ∈ R. A Jordan *-derivation of R is called X-inner if it is of the form x ↦ xa - ax* for x ∈ R, where a ∈ Qms(R).
Lee, Tsiu-Kwen, Zhou, Yiqiang
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Derivations in prime rings.

2000
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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2-PRIME IDEALS AND 2-PRIME RINGS

JP Journal of Algebra, Number Theory and Applications, 2021
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Prime Quantifier Eliminable Rings

Journal of the London Mathematical Society, 1980
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PIECEWISE PRIME RINGS

Mathematics and Mathematics Education, 2002
Gary F. Birkenmeier, Jae Keol Park
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Generalized derivations of prime rings.

2019
The authors extend to generalized derivations some known results for derivations acting on prime rings. Let \(R\) be a prime ring with center \(Z\) and extended centroid \(C\). Call \((d,\alpha)\) a generalized derivation of \(R\) when \(\alpha\in\text{Der}(R)\), \(d\colon R\to R\) is additive, and \(d(xy)=d(x)y+x\alpha(y)\) for all \(x,y\in R\). Among
Albaş E., Argaç N.
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Fully \(^*\)-prime rings with involution

2018
Let \(R\) be an associative ring, not necessarily unital. An involution \(*\) on \(R\) is an additive map on \(R\) such that \((a^*)^*=a\) and \((ab)^*=b^*a^*\) for every \(a\), \(b\in R\). The author studies properties of \(*\)-prime rings, that is rings with involution.
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ON DERIVATIONALLY PRIME RINGS

Russian Mathematical Surveys, 1980
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Prime Cyclic Rings

International Journal of Mathematics Trends and Technology, 2016
Meram Munirathnam, Dr. D Bharathi
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