GRUP RING

Abstract

The RG ring group is the set formed from group G below multiplication operations of finite elements and commutative rings. R with elements unit. If defined the operation of addition and operation of doubling in RG respectively                      i I i i i i I i i i I i a g a g (a b) g and                           i I i g g g j k i I i i i I i i g a b g a b g j k i () for each a g b g RG i I i i i I i i      , then RG is a ring. Based on the definition of RG formed from two structures that have certain properties, then the properties of RG depend on R and G forming them, namely: a. Every element in R is commutative with each element in RG and in unit elements R is a unit element in RG b. Every element in G has a doubling inverse in RG c. RG is commutative if and only if G is commutative d. If S subring of R and H subgroups of G, then SG and RH are subring-subring from RG.