Semiring framework for the theory of mobility index

There is given first a short overview of the theory of mobility index used in social sciences, economics, education, politics, etc. Shorrocks [38] introduced several properties (criteria) for mobility indices, which can be taken into three classes. There is given in this paper an initial framework for some general mathematical explanations for the notions used in the theory of mobility, putting all in the semiring framework. In the theory of mobility matrices are considered as equal with respect to the mobility if they have equal mobility measures, which correspond in mathematics to factor spaces. It is shown that the basic known mobility indices satisfy the required conditions.