ON GENERALIZATION OF $Rad-D_{11}$-MODULE

Abstract

Abstract. This paper gives generalization of a notion of supplemented module. Here, we utilize some algebraic properties like supplemented, amply supplemented and local modules in order to obtain the generalization. Other properties that are instrumental in this generalization are D i , SSP and SIP . If a module M is Rad-D 11 -module and has D 3 property, then M is said to be completely-Rad-D 11 -module (C-Rad-D 11 -module). Similarly it is for M with SSP property. We provide some conditions for a supplemented module to be C-Rad-D 11 -module. Introduction and PreliminariesThroughout this paper all rings are unital and modules are considered to be right