Modules with few types over a hereditary Noetherian prime ring (Q2732278)

The author establishes Vaught's Conjecture for modules over certain rings. In the first part of the paper the author proves a variety of results on modules being divisible, \(\omega\)-stable and having few types under conditions on the ring of having a classical quotient ring, being semiprime and being semihereditary.NEWLINENEWLINENEWLINEIt is shown in the second part that every module with few types over a countable hereditary noetherian prime ring is \(\omega\)-stable and hence that Vaught's Conjecture is true for modules over such rings. This extends the previously known case [\textit{V. Puninskaya}, ``Vaught's conjecture for modules over a Dedekind prime ring'', Bull. Lond. Math. Soc. 31, 129-135 (1999; Zbl 0921.03043)] of Dedekind prime rings.