Extension of Santilli's isotopies to non-injective isoalgebras

Abstract

Santilli's isotopies constitute a new branch of mathematics characterized by axiom-preserving isotopic lifting of units, products, numbers, fields, topologies, geometries, algebras, groups, etc., with numerous novel applications in physics, chemistry and other quantitative sciences. The continuation of these studies requires deeper research on non-injective isotopies. The main goal of this paper is to generalize the usual isotopic construction model to obtain non-injective isoalgebras, by using so many new laws * and isounities in the general set associated with the Santilli's isotopy, as laws has the initial structure. In this way, the study of the properties of this general set is very useful. In fact, this study constitutes the MCIM isotopic construction model, which has been studied by the authors since 2001. In this model, there are a main isounit and a main *-law, which determine the mathematical isostructure, and some secondaries ones, which determine the laws in this isostructure. So, the study of all these elements can determine how to build a non-injective isotopy, by taking into consideration the different factors on which the main isounit depends.