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.

Let C be a non-empty class of modules closed under isomorphic copies. We consider some classes of modules associated to C. Among them, we study two important classes in the theory of natural and conatural classes of modules, namely the class consisting of all modules having no non-zero submodule in C, as well as its dual.

We determine the characters of the simple composition factors and the submodule lattices of certain Weyl modules for classical groups. The results have several applications. The simple modules arise in the study of incidence systems in finite geometries and knowledge of their dimensions yields the p-ranks of these incidence systems.

Let S be a polynomial ring in n variables over a field K of characteristic 0. A numerical characterization of all possible extremal Betti numbers of any graded submodule of a finitely generated graded free S-module is given. 2010 Mathematics Subject Classification: 13B25, 13D02, 16W50.

For σ−PWB extensions, we extend to modules the theory of Gröbner bases of left ideals presented in [5]. As an application, if A is a bijective quasi-commutative σ − PWB extension, we compute the module of syzygies of a submodule of the free module A.

Let R be a commutative ring with identity and M be a unital R-module. Then M is called a multiplication module provided for every submodule N of M there exists an ideal I of R such that N = IM. Our objective is to investigate properties of prime and semiprime submodules of multiplication modules. Mathematics Subject Classification: 13C05, 13C13

A tag module is a generalization, in any abelian category, of a torsion abelian group. The theory of such modules is developed, it is shown that countably generated tag modules are simply presented, and that Ulm's theorem holds for simply presented tag modules. Zippin's theorem is stated and proved for countably generated tag modules. 1. TAG-modules In the theory of torsion abelian groups, a di...

B. Magajna and J. Schweizer showed in 1997 and 1999, respectively, that C*-algebras of compact operators can be characterized by the property that every norm-closed (and coinciding with its biorthogonal complement, resp.) submodule of every Hilbert C*-module over them is automatically an orthogonal summand. We find out further generic properties of the category of Hilbert C*-modules over C*-alg...