new model of invertible elements on multiplicative sample of quasilinear spaces

Invertible members of some of the most famous multiplicative quasilinear spaces are exactly equal to invertible elements of the linear subspace of such spaces. but with the old definition of invertible elements, we do not get anything extra. so, in the present paper, we develop the introductory algebra and introduce an extended model of invertible elements. this new concept plays a fundamental role in the definition of the generalized spectrum model. these new objects are constructed in such a way that can provide acceptable results. for example, we will be able to generalize the well-known theorem ``spectral mapping property for polynomials’’ with these new notions.