Enumeration of Involutions of Finite Rings

In this paper, we study a special class of elements in the finite commutative rings called involutions. An involution ring R is an element with property that x^2-1=0 for some x R. This describes both implementation and enumeration involutions various rings, such as cyclic non-cyclic zero-rings, fields, especially Gaussian integers. The paper begins simple well-known results equation over It provides concrete setting to enumerate R, along isomorphic relation I(R)≅Z_2^k.