In an earlier paper a construction was given for an infinite-dimensional uniserial module over Q for SL(2,Z) whose composition factors are all isomorphic to the standard (two-dimensional) module. In this note we consider generalizations of this construction to other composition factors and to other rings of algebraic integers.

Let Λ be a commutative local uniserial ring of length n, p a generator of the maximal ideal, and k the radical factor field. The pairs (B, A) where B is a finitely generated Λ-module and A ⊆ B a submodule of B such that pmA = 0 form the objects in the category Sm(Λ). We show that in case m = 2 the categories Sm(Λ) are in fact quite similar to each other: If also ∆ is a commutative local uniseri...

A right module M over an associative ring with unity is a QTAG-module if every finitely generated submodule of any homomorphic image of M is a direct sum of uniserial modules. In this paper we find a suitable condition under which a special ω-elongation of a summable QTAG-module by a ( ω +k)-projective QTAG-module is also a summable QTAG-module.