ON THE QUASIMODULES AND NORMED QUASIMODULES

Abstract

In this paper, we give definition of quasiring as a new concept. Also, we introduce the notions of quasimodule and normed quasimodule defined on a quasiring. We should immediately note that a quasimodule is a generalization of quasilinear spaces. Similarly, normed quasimodule is a generalization of normed quasilinear spaces defined by Aseev, [3]. Moreover, we obtain some results about the relationships between these concepts. We think that investigations on quasimodules may provide some important contributions to improvement of some branches of quasilinear functional analysis such as the duality theory of quasilinear spaces. Also we recognize that the notion of quasimodule is more suitable backdrop as regards theory of quasilinear spaces in examination of quasilinear functional.