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Let $R$ be a prime ring with its Utumi ring of quotients $U$ and extended centroid $C$ . Suppose that $F$ is a generalized derivation of $R$ and $L$ is a noncentral Lie ideal of $R$ such that $F (u) {[F (u), u]}^{n} = 0$ for all $u \in L$ , where $n \geq 1$ is a fixed integer. Then one of the following holds: (1) ...

Generalized Derivations on (Semi-)Prime Rings and Noncommutative Banach Algebras

Feng Wei, Zhankui Xiao (2009)

Rendiconti del Seminario Matematico della Università di Padova

Generalized Derivations with Power Central Values on Multilinear Polynomials on Right Ideals

Nurcan Argaç, Vincenzo De Filippis, H. G. Inceboz (2008)

Rendiconti del Seminario Matematico della Università di Padova

Generalized flatness and coherence

Hana Jirásková (1980)

Commentationes Mathematicae Universitatis Carolinae

Generalized periodic and generalized Boolean rings.

Bell, Howard E., Yaqub, Adil (2001)

International Journal of Mathematics and Mathematical Sciences

Generalized primary rings and ideals.

Gorton, Christine, Heatherly, Henry (2006)

Mathematica Pannonica

Generalized projectivity

Hana Jirásková, Josef Jirásko (1978)

Czechoslovak Mathematical Journal

Generalized projectivity. II.

Josef Jirásko (1979)

Commentationes Mathematicae Universitatis Carolinae

Generalized radical rings, unknotted biquandles, and quantum groups

Wolfgang Rump (2007)

Colloquium Mathematicae

Generalized radical rings (braces) were introduced for the study of set-theoretical solutions of the quantum Yang-Baxter equation. We discuss their relationship to groups of I-type, virtual knot theory, and quantum groups.

Generalized reverse derivations and commutativity of prime rings

Shuliang Huang (2019)

Communications in Mathematics

Let $R$ be a prime ring with center $Z (R)$ and $I$ a nonzero right ideal of $R$ . Suppose that $R$ admits a generalized reverse derivation $(F, d)$ such that $d (Z (R)) \neq 0$ . In the present paper, we shall prove that if one of the following conditions holds: (i) $F (x y) \pm x y \in Z (R)$ , (ii) $F ([x, y]) \pm [F (x), y] \in Z (R)$ , (iii) $F ([x, y]) \pm [F (x), F (y)] \in Z (R)$ , (iv) $F (x \circ y) \pm F (x) \circ F (y) \in Z (R)$ , (v) $[F (x), y] \pm [x, F (y)] \in Z (R)$ , (vi) $F (x) \circ y \pm x \circ F (y) \in Z (R)$ for all $x, y \in I$ , then $R$ is commutative.

Gorenstein tiled orders with hereditary ring of multipliers of Jacobson radical.

Kirichenko, Vladimir V., Khibina, Marina A., Zhuravlev, Viktor N. (2001)

Analele Ştiinţifice ale Universităţii “Ovidius" Constanţa. Seria: Matematică

Group Rings of Circle and Unit Groups.

Robert Sandling (1974)

Mathematische Zeitschrift

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