MULTIPLICATIVE n-TH ROOT FUNCTIONS OVER FINITE SEMIGROUPS, GROUPS, FIELDS AND COMMUTATIVE RINGS

In this paper, we study the existence and uniqueness of multiplicative n-th root functions n √ over finite semigroups, in order to implement these ideas on finite groups, fields and commutative rings. A set of sufficient and necessary conditions are presented for existence of multiplicative n-th root functions over different algebraic structures. It is also shown that once the existence is established, the uniqueness is guaranteed. In addition, we describe the construction procedure of such a function.