Definable modules over definable rings without zero divisors in o-minimal structures

Abstract

In an o-minimal structure, every definable group admits a definable group manifold. Moreover, one can also show an analogue of this statement for definable rings. In this work, we prove that every definable module over definable ring without zero divisors admits a definable module manifold. In addition, we also give the classification of definable modules over definable rings without zero divisors in o-minimal structures