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On generalized derivations of partially ordered sets. (English) Zbl 1469.06002

Summary: 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.

MSC:

06A06 Partial orders, general
06A11 Algebraic aspects of posets
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