Abstract

The set of some real rhotrices of the same dimension D ∗ was defined in [2] to be an integral domain. An example of a finite field M [R3] was given in [4] based on this definition also and on the construction of finite fields presented in [3]. It was discovered that the finite sub collection of the elements of M [R3] as contained in D∗ is not closed under rhotrix addition and hence not an integral domain. More generally, D∗ is not an integral domain as it is not closed under rhotrix addition. This problem affects the field of fractions constructed in [8]. A solution to this problem is provided in this article and the construction method of such fields is reviewed. This reviewed version gives the generalization of such construction as the n-dimensional rhotrices are used.