THE THIRD GROUP OF UNITS OF THE RING
Let R be a finite commutative ring with identity and let be its group of units. El-Kassar and Chehade [2] showed that supports a ring structure, thus they defined the second group of units of the ring R denoted by and the kth group of units of the ring R defined iteratively as They discussed the case when and In this paper, we examine the structure of the third group of units of the ring We solve the problem in determining all rings having the third group of units trivial and cyclic.
finite commutative rings, group of units, cyclic groups.