Bull Braz Math Soc, New Series 36(2), 187-196 © 2005, Sociedade Brasileira de Matemática The general set in the MCIM Isotopic Model R. M. Falcón and J. Núñez Abstract. To obtain a bigger number of mathematical and physical applications of the Santilli’s isotheory, the latest studies have shown the necessity of analyzing isotopic models which use non associative laws. The main goal of this paper is to give a gener- alization of the isotopic construction model based on the multiplication (MCIM), which is useful to obtain non associative mathematical isostructures. Keywords: Santilli’s Isotheory, isotopic model, isostructure. Mathematical subject classification: 03H05, 08A05, 03C65. Introduction In 1978, R. M. Santilli proposed a generalization of the conventional Lie’s theory by using isotopies. The isotopies of Lie’s theory were constructed to lift the theory from its current sole applicability to linear systems to nonlinear systems, lifting achieved via the reconstruction of linearity on isospaces over isofields. It was the first stage of what is actually known as Santilli’s Isotheory [1]. He considered that the basic unit I of each mathematical structure can depend on several factors external to the system in which we are placed, like coordinates, speed, time, density, temperature, and so on. It involves an isounit of the type  I =  I (x ,v, t , μ, τ, ...). By using this principle, Santilli carried out a step by step construction which generalizes the most common mathematical structures, originating those denominated mathematical isostructures [2], [3]. It allowed him to progress in the development of some physical applications, mainly in Quantum Mechanics and Dynamics of Particles [4]. In 2001, the isotopic construction model based on the multiplication (from now on, it will be denoted by MCIM) was introduced by ourselves (see [5]) in the same way as the one proposed by Santilli, although by putting a special emphasis in the use of *-laws. Later, it was improved in [6] and [7]. Nevertheless, to enlarge the number of mathematical isostructures and to get new practical applications, it is necessary to weaken the associativity hypothesis, obtaining in this way more Received 7 July 2004.