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...

We describe the structure, including composition factors and submodule lattices, of cross-characteristic permutation modules for the natural actions of the orthogonal groups O± m(3) with m ≥ 6 on nonsingular points of their standard modules. These actions together with those studied in [2] are all examples of primitive rank 3 actions of finite classical groups on nonsingular points.

Given a Young diagram λ and the set Hλ of partitions of {1, 2, . . . , |λ|} of shape λ, we analyze a particular S|λ|-module homomorphism QH λ → QHλ ′ to show that QHλ is a submodule of QHλ ′ whenever λ is a hook (n, 1, 1, . . . , 1) with m rows, n ≥ m, or any diagram with two rows.

Let k[V ] be the space of functions from a finite vector space into the algebraically closure of its field of scalars. This paper describes the lattice of subspaces of k[V ] which are invariant under the affine group AGL(V ). The description provides a simple method for finding the submodule generated by any set of functions given as polynomials in the standard coordinates.

Let R be a universally catenary locally equidimensional Noetherian ring. We give a multiplicity based criterion for an arbitrary finitely generated R-module to be integral over a submodule. Our proof is self-contained and implies the previously known numerical criteria for integral dependence of ideals and modules.