Extending properties of E(S3) near-ring

In this thesis, the extending and Baer conditions of E(S3), whose additive group is generated by endomorphisims of the group S3, a symmetric group of 6th order, and which has a right near-ring structure with addition and composition operation, were investigated. For this purpose, we first presented the basic concepts and theorems of the near-ring theory that will be used in our study. In the third section, the extending and Baer conditions on near-rings were given. Examples which satisfy and do not satisfy these conditions were presented. In the fourth section, the subgroups of the near-ring E(S3) were given. It was also computed that the left annihilators of each idempotent element and the N-subgroup structures generated by these idempotent elements. In the fifth section, the left annihilators of the appropriate T subsets of S3 were computed and the left ideal structures of the near-ring E(S3) were studied in detail. In the last section, it was shown that the near-ring E(S3) does not satisfy neither the extending nor the Baer conditions.