Khaldoun Al-Zoubi, Shatha Alghueiri, Ece Y. Celikel
(2020)
Commentationes Mathematicae Universitatis Carolinae
Let be a group with identity and let be a -graded ring. In this paper, we introduce and study the concept of graded -ideals of . A proper graded ideal of is called a graded -ideal of if whenever where , then either or or . We introduce several results concerning --ideals. For example, we give a characterization of graded -ideals and their homogeneous components. Also, the relations between graded -ideals and others that already exist, namely, the graded prime ideals,...
We investigate a new type of generalized derivations associated with Hochschild 2-cocycles which was introduced by A. Nakajima. We show that every generalized Jordan derivation of this type from CSL algebras or von Neumann algebras into themselves is a generalized derivation under some reasonable conditions. We also study generalized derivable mappings at zero point associated with Hochschild 2-cocycles on CSL algebras.
Let be a prime ring with its Utumi ring of quotients and extended centroid . Suppose that is a generalized derivation of and is a noncentral Lie ideal of such that for all , where is a fixed integer. Then one of the following holds:
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An R-algebra A is called an E(R)-algebra if the canonical homomorphism from A to the endomorphism algebra of the R-module , taking any a ∈ A to the right multiplication by a, is an isomorphism of algebras. In this case is called an E(R)-module. There is a proper class of examples constructed in [4]. E(R)-algebras arise naturally in various topics of algebra. So it is not surprising that they were investigated thoroughly in the last decades; see [3, 5, 7, 8, 10, 13, 14, 15, 18, 19]. Despite...
Mohammad Ashraf, Nazia Parveen, Bilal Ahmad Wani
(2017)
Communications in Mathematics
Let be the triangular algebra consisting of unital algebras and over a commutative ring with identity and be a unital -bimodule. An additive subgroup of is said to be a Lie ideal of if . A non-central square closed Lie ideal of is known as an admissible Lie ideal. The main result of the present paper states that under certain restrictions on , every generalized Jordan triple higher derivation of into is a generalized higher derivation of into .
In this paper, we investigate a new type of generalized derivations associated with Hochschild 2-cocycles which is introduced by A.Nakajima (Turk. J. Math. 30 (2006), 403–411). We show that if is a triangular algebra, then every generalized Jordan derivation of above type from into itself is a generalized derivation.