“…Since the early 2000s there has been increased interest -and several new significant results -in the study of Kurosh-type and related problems for associative algebras; see, e.g., [3], [16], and [18] for an introduction and overview. A thumbnail sketch of relevant developments could include: Smoktunowicz's 2002 construction of a simple nil ring over an arbitrary countable field [15]; Bell and Small's 2002 construction of a finitely generated primitive algebraic algebra over an arbitrary field [2]; Lenagan and Smoktunowicz's 2007 construction of an infinite dimensional nil algebra, over an arbitrary countable field, of finite Gelfand-Kirillov (GK-) dimension [9]; Lenagan, Smoktunowicz, and Young's 2012 construction of an infinite dimensional nil algebra, over an arbitrary countable field, of GK-dimension at most three [10]; and Bell, Small, and Smoktunowicz's construction of an infinite dimensional primitive algebraic algebra, over an arbitrary countable field, of GK-dimension at most six [3].…”