The invention relates to highly dense transparent aluminum oxide (alumina) and structures thereof for applications where, e.g. in the lighting industry, a fine crystal size has to be obtained and stabilized for use at temperatures of 800°C or more. The invention also relates to an electric lamp having a discharge tube with a wall of such a ceramic. The alumina according to the invention is provided with an additive and has an average crystal size = 2µm, and a relative density higher than 99.95% with a real in-line transmission RIT = 30%, preferably > 40% and more preferably > 50%, measured over an angular aperture of at most 0.50 at a sample thickness of 0.8 mm and with a single wave-length of light λ of preferably 645nm, and the additive comprises at least one of the substances from the group consisting of oxides of Mg, Y, Er and La.