Pseudo Rho-Algebras in Fields with their Applications Using Polynomials with Two Variables

The main purpose of this work is to present the concept of pseudo Rho-algebra as a generalization of the Rho-algebra. We investigate this type behaves nicely in terms of common mappings like homomorphisms and direct products. In fact, we can show identify kernel objects and the fundamental theorem of homomorphisms using Rho-ideals in this theory. Also, some important classes of pseudo Rho-algebra and their applications are investigated and studied. Moreover, the necessary characteristics for or tantamount to membership in major subtypes of pseudo Rho/d-algebras under these cases are identified. The Rho/d-algebras and pseudo Rho/d-algebras are generated using some new classes of polynomials with two variables that are introduced in this work, like commutative identical, associative identical, regular identical, proper conditionally identical, and improper conditionally identical. Finally, the category of pseudo Rho/d-algebras can be classified using a conditionally couple, giving us additional flexibility in dealing with two different fields.