The Transcendence Degree over a Ring

For a finitely generated algebra over a field, the transcendence degree is known to be equal to the Krull dimension. The aim of this paper is to generalize this result to algebras over rings. A new definition of the transcendence degree of an algebra A over a ring R is given by calling elements of A algebraically dependent if they satisfy an algebraic equation over R whose trailing coefficient, with respect to some monomial ordering, is 1. The main result is that for a finitely generated algebra over a Noetherian Jacobson ring, the transcendence degree is equal to the Krull dimension

Stellar dust production and composition in the Magellanic Clouds

The dust reservoir in the interstellar medium of a galaxy is constantly being replenished by dust formed in the stellar winds of evolved stars. Due to their vicinity, nearby irregular dwarf galaxies the Magellanic Clouds provide an opportunity to obtain a global picture of the dust production in galaxies. The Small and Large Magellanic Clouds have been mapped with the Spitzer Space Telescope from 3.6 to 160 {\mu}m, and these wavelengths are especially suitable to study thermal dust emission. In addition, a large number of individual evolved stars have been targeted for 5-40 {\mu}m spectroscopy, revealing the mineralogy of these sources. Here I present an overview on the work done on determining the total dust production rate in the Large and Small Magellanic Clouds, as well as a first attempt at revealing the global composition of the freshly produced stardust.Comment: accepted for publication by Earth, Planets & Spac

Impact of the Agricultural Sector on the Arkansas Economy in 2003

Agriculture and associated agricultural activities are major contributors to the Arkansas economy. Agriculture is defined as the sum of agricultural production and processing activities, unless otherwise specified, and includes crop and animal production and processing, agricultural support industries, forestry and forest products, and textile goods. Agriculture contributes to the economy through direct agricultural production and value-added processing, and also leads to economic activity in other parts of the economy