Enumeration of Involutions of Finite Rings
Authors : Sajana Shaik, Chalapathi Tekuri
Pages : 64-74
Doi:10.53570/jnt.971924
View : 11 | Download : 6
Publication Date : 2021-09-30
Article Type : Research
Abstract :In this paper, we study a special class of elements in the finite commutative rings called involutions. An involution of a ring R is an element with the property that x^2-1=0 for some x in R. This study describes both the implementation and enumeration of the involutions of various rings, such as cyclic rings, non-cyclic rings, zero-rings, finite fields, and especially rings of Gaussian integers. The paper begins with simple well-known results of an equation x^2-1=0 over the finite commutative ring R. It provides a concrete setting to enumerate the involutions of the finite cyclic and non-cyclic rings R, along with the isomorphic relation I(R)≅Z_2^k.Keywords : Cyclic rings, noncyclic rings, zero rings, finite fields, involutions