ON GROUP NEAR-RING MODULES

Abstract

It is shown that any R[G]-ideal (-submodule) of R(^G) is contained in an R[G]-ideal (-submodule) of the form R(^G) where L is a left ideal (left R-subgroup) of the near-ring R. For a connected R-module N an R[G]-module structure is denned on N(^G) such that if the near-ring R is 1-primitive on R^N then N(^GM) is a faithful monogenic R[G]-module. Furthermore it is shown that if N is a connected R-module then there is a monomorphism from End_R ^N into End _R[G] ^N[G] (as monoids). Finally a relationship is given between the J½- and J ₀-radical of the near-ring R.