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Jordan ideals and derivations in prime near-rings

Abdelkarim Boua; Lahcen Oukhtite; Abderrahmane Raji — 2014

Commentationes Mathematicae Universitatis Carolinae

In this paper we investigate $3$ -prime near-rings with derivations satisfying certain differential identities on Jordan ideals, and we provide examples to show that the assumed restrictions cannot be relaxed.

On generalized derivations of partially ordered sets

Ahmed Y. Abdelwanis; Abdelkarim Boua — 2019

Communications in Mathematics

Let $P$ be a poset and $d$ be a derivation on $P$ . In this research, the notion of generalized $d$ -derivation on partially ordered sets is presented and studied. Several characterization theorems on generalized $d$ -derivations are introduced. The properties of the fixed points based on the generalized $d$ -derivations are examined. The properties of ideals and operations related with generalized $d$ -derivations are studied.

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