Some Remarks on Rings

Algebraic structures such as Rings, Fields, Boolean Algebras (Set Theory) and \(\sigma\)-Fields are well known and much has been written about them. In this paper we explore some properties of rings related to the distribution law. Specifically, we shall show that for rings there exists only one distribution law. Moreover, for the ring \((Z_{p(p−1)n} +, \cdot)\), where \((p, n) = 1\) there exist isomorphic groups \((G, +)\), \((H, \cdot)\), \(G, H \subset Z_{p(p−1)n}\) of the order \((p − 1)\). Finally, we note that every ring \((Z_{pn}, +, \cdot)\) contains subfields \(\text{mod}(pn)\).