Page Introduction 269 Notation and terminology 271 I. Basic facts 271 1. Review of IM 271 2. Review of AM 273 3. Solvable groups, aG, finite Priifer rank, FP 2 , and HNN-extensions . 276 4. Matrix computation of AM in the finite rank case . . . . 277 5. Finiteness conditions: F P m and finite presentation . . . . 278 6. The properties m-tameness and w-domestication 280 II. Proof that Hm{G, Y\ R...

Let g be a semisimple complex Lie algebra and k ⊂ g be any algebraic subalgebra reductive in g. For any simple finite dimensional k-module V , we construct simple (g, k)-modules M with finite dimensional k-isotypic components such that V is a k-submodule of M and the Vogan norm of any simple k-submodule V ′ ⊂ M, V ′ 6≃ V , is greater than the Vogan norm of V . The (g, k)-modules M are subquotie...

A combination of crystallography, biochemistry, and gene expression analysis identifies the coactivator subcomplex Med8C/18/20 as a functionally distinct submodule of the Mediator head module. Med8C forms a conserved alpha-helix that tethers Med18/20 to the Mediator. Deletion of Med8C in vivo results in dissociation of Med18/20 from Mediator and in loss of transcription activity of extracts. De...

The Hardy space on the unit ball in C provides examples of a quasi-free, finite rank Hilbert module which contains a pure submodule isometrically isomorphic to the module itself. For n = 1 the submodule has finite codimension. In this note we show that this phenomenon can only occur for modules over domains in C and for finitely-connected domains only for Hardy-like spaces, the bundle shifts. M...

Continuing our earlier investigation [15] of the essential normality of submodules generated by polynomials, the emphasis of this paper is on submodules of the Drury-Arveson module H n. In the case of two complex variables, we show that for every polynomial q ∈ C[z1, z2], the submodule [q] of H 2 is p-essentially normal for p > 2. In the case of three complex variables, we show that there is a ...

In this paper, we introduce the concept of a quasi-radical semi prime submodule. Throughout work, assume that is commutative ring with identity and left unitary R- module. A proper submodule called (for short Q-rad-semiprime), if for , ,and then . Where intersection all submodules