Search

Separable equivalence of algebras was introduced by Markus Linckelmann in [Linllb] and may be considered as an extension to the more well-known concepts of Morita, stable and derived equivalence. We will generalise the idea of separable equivalence of algebras to additive categories and demonstrate how a separable equivalence between algebras provides separable equivalences between several related categories. We will prove that there are several properties of an algebra that are invariant under separable equivalence. Specifically we show that if two algebras are separably equivalent then they must have the same complexity. We also show that the representation type of an algebra is preserved, including the finer grain classes of domestic and polynomial growth. Finally, if G is a finite group with elementary abelian Sylow p-subgroup P, then we use the separable equivalence of kG and kP to provide an upper bound for the representation dimension of kG, where k is an algebraically closed field of characteristic p.

The adsorption of sulphate has been studied using alpine and sub-alpine podzolic soils from the Allt a'Mharcaidh catchment, Cairngorms, Scotland, U.K. A detailed investigation of sulphur pools and mechanisms of sulphur retention has revealed that incoming sulphate ion, both marine and anthropogenic, is being retained by a range of adsorption mechanisms. Analysis of the soils has indicated that the sulphur content of the soils is dominated by organic forms of sulphur. Selective chemical fractionation techniques have identified an accumulation of sesquioxides, dominated by amorphous aluminium, in the basal horizons of all the soil profiles. Adsorption of sulphate has been shown to be mainly governed by the quantity and variable charge character of this sesquioxide phase. Fractionation has also suggested that the sesquioxides in the basal horizons of the soils are dominated by a combination of gibbsitic and imogolitic materials, the latter being present as a result of podzolization processes. The generation of sulphate adsorption isotherms has revealed that the organic horizons of the catchment soils show little or no sulphate adsorption capacity, due to a small sesquioxide content. In contrast, the mineral horizons are all capable of adsorbing sulphate, and in most cases this adsorption can be modelled to the Langmuir adsorption equation. The adsorption capacity of particle size fractions of the soils has revealed that even soil particles > 1 mm show an ability to retain sulphate, possibly by physical entrapment of soil solution in mineral pores or amorphous silica gel coatings. The accompanying hydroxyl release that is generally assumed to accompany adsorption of sulphate in the mineral soils was not evident, and unless a ligand exchange reaction was masked by other chemical reactions involving total proton balance, sulphate adsorption in the catchment soils is not due to a specific or 'low affinity' specific mechanism.