Hierarchical galaxy formation models predict the development of elliptical galaxies through a combination of the mergers and interactions of smaller galaxies. We are carrying out a study of Early-Type Galaxies (ETGs) using GAMA multi-wavelength and Herschel-ATLAS sub-mm data to understand their intrinsic dust properties. The dust in some ETGs may be a relic of past interactions and mergers of galaxies, or may be produced within the galaxies themselves. With this large dataset we will probe the properties of the dust and its relation to host galaxy properties. This paper presents our criteria for selecting ETGs and explores the usefulness of proxies for their morphology, including optical colour, Sérsic index and Concentration index. We find that a combination of criteria including r band Concentration index, ellipticity and apparent sizes is needed to select a robust sample. Optical and sub-mm parameter diagnostics are examined for the selected ETG sample, and the sub-mm data are fitted with modified Planck functions giving initial estimates for the cold dust temperatures and masses.

Let K be a field of characteristic 0, which is algebraically closed to radicals. Let F = K((X)) be the valued field of Laurent power series and let G = Aut(F/K). We prove that if L is a subfield of F, K ≠ L, such that L/K is a sub-extension of F/K and F/L is a Galois algebraic extension (L/K is Galois coalgebraic in F/K), then L is closed in F, F/L is a finite extension and Gal(F/L) is a finite cyclic group of G. We also prove that there is a one-to-one and onto correspondence between the set of all finite subgroups of G and the set of all Galois coalgebraic sub-extensions of F/K. Some other auxiliary results which are useful by their own are given.

If K is a field with a non-trivial non-Archimedean absolute value (multiplicative norm) | |, we describe all non-Archimedean K-algebra norms on the polynomial algebra K[X1, . . . , Xr] which extend | |.

The generating degree $\text{g}\deg \left( A \right)$ of a topological commutative ring $A$ with char $A\,=\,0$ is the cardinality of the smallest subset $M$ of $A$ for which the subring $\mathbb{Z}\left[ M \right]$ is dense in $A$ . For a prime number $p$ , ${{\mathbb{C}}_{p}}$ denotes the topological completion of an algebraic closure of the field ${{\mathbb{Q}}_{p}}$ of $p$ -adic numbers. We prove that $\text{g}\deg \left( {{\mathbb{C}}_{p}} \right)\,=\,1$ , i.e., there exists $t$ in ${{\mathbb{C}}_{p}}$ such that $\mathbb{Z}\left[ t \right]$ is dense in ${{\mathbb{C}}_{p}}$ . We also compute $\text{gdeg}\left( A\left( U \right) \right)$ where $A\left( U \right)$ is the ring of rigid analytic functions defined on a ball $U$ in ${{\mathbb{C}}_{p}}$ . If $U$ is a closed ball then $\text{gdeg}\left( A\left( U \right) \right)\,=\,2$ while if $U$ is an open ball then $\text{gdeg}\left( A\left( U \right) \right)$ is infinite. We show more generally that $\text{gdeg}\left( A\left( U \right) \right)$ is finite for any affinoid $U$ in ${{\mathbb{P}}^{1}}\left( {{\mathbb{C}}_{p}} \right)$ and $\text{gdeg}\left( A\left( U \right) \right)$ is infinite for any wide open subset $U$ of ${{\mathbb{P}}^{1}}\left( {{\mathbb{C}}_{p}} \right)$ .