One-sided Grothendieck quotients

We introduce one-sided thick subcategories of an arbitrary preadditive category and define a quotient category . When is abelian, this concept specializes to Grothendieck’s quotient for two-sided thick . We determine the left noetherian rings for which the injective modules form a left thick subcategory. We exhibit a class of one-sided thick subcategories in categories of coherent functors which are ubiquitous in representation theory. Received: 14 November 2006 Revised: 12 March 2007