Bimultipliers of R-algebroids

Abstract

Group action is determined bythe automorphism group and algebra action is defined by the multiplication algebra. In the study we generalize the multiplication algebra by defining multipliers of an R-algebroid M. Firstly, the set of bimultipliers on an R-algebroid is introduced, it is denoted by Bim(M), then it is proved that this set is an R-algebroid, it is called multiplication R-algebroid. Using this Bim(M), for an R-algebroid morphism A → Bim(M) it is shown that this morphism gives an R-algebroid action. Then we examine some of the properties associated with this action.