Note on Generalized Jordan Higher Left Centralizers With Hochschild 2-cocycles

Abstract

In this paper, we introduced  new definitions which are definitions of generalized higher left centralizer mappings and generalized Jordan higher left centralizer mappings associated with Hochschild 2-Cocycle and also we show that every generalized Jordan higher left centralizer associated with Hochschild 2-Cocycle is a generalized higher left centralizer under certain condition.