For a compact Hausdorff abelian group K and its subgroup H ≤ K, one defines the g-closure g K (H) of H in K as the subgroup consisting of χ ∈ K such that χ(a n) −→ 0 in T = R/Z for every sequence {a n } inˆK (the Pontryagin dual of K) that converges to 0 in the topology that H induces onˆK. We prove that every countable subgroup of a compact Hausdorff group is g-closed, and thus give a positive...

Maarten V. de Hoop,1 Robert D. van der Hilst2 and Peng Shen3 1Center for Computational and Applied Mathematics, Purdue University, 150 N. University Street, West Lafayette IN 47907, USA 2Department of Earth, Atmospheric and Planetary Sciences, Massachusetts Institute of Technology, Rm 54-517A, Cambridge, MA 02139, USA. E-mail: [email protected] 3Total E&P USA, 800 Gessner, Suite 700, Houston TX 702...

The affinoid envelope, $\widehat{U(\mathcal{L})}$ of a free, finitely generated $\mathbb{Z}_p$-Lie algebra $\mathcal{L}$ has proven to be useful within the representation theory compact $p$-adic Lie groups. Our aim is further understand algebraic structure $\widehat{U(\mathcal{L})}$, and this end, we will define Dixmier module over prove that object generally irreducible in case where nilpotent...

Let $\mathfrak a$ be an ideal of a commutative Noetherian ring $R$ and $t$ non-negative integer. $M$ $N$ two finitely generated $R$-modules. In certain cases, we give some bounds under inclusion for the annihilators $\operatorname{Ext}^t_R(M, N)$ $\operatorname{H}^t_{\mathfrak a}(M)$ in terms minimal primary decomposition zero submodule which are independent choice decomposition. Then, by using...