New view of homomorphic properties in BCK-algebra. A New View of Homomorphic Properties of BCK-Algebra in Terms of Some Notions of Discrete Dynamical System

      Аннотация: In this book we analyze the properties of some notions such as fixed points, periodic points, invariant set and strongly invariant set of Discrete Dynamical System and infuse these notions in BCK-algebra for determining a new class of homomorphic properties as well as new sets which are to be BCK-sub algebras and BCK-ideals. The concept of Discrete Dynamical System in BCK-algebra will establish a foundation for further investigation concerning the development of BCK-algebras and their applications in other disciplines of algebra. The results of this concept will enable the researchers to characterize other classes of BCK-algebra and to insert this concept to some further algebraic structures and to consider the results of this concept to some possible applications in information systems and computer sciences. We have no doubt that the research along this line can be kept up and indeed some results in this book have already made up a foundation for further exploration concerning the further progression of discrete dynamical system in BCK-algebra and their applications in other disciplines of algebra.

Ключевые слова: BCK-Algebra, Discrete dynamical system, Periodic points, Fixed Points, Invariant set, S-invariant or (Strongly invariant) set