“…A nil element is obviously algebraic, and, in the converse direction, it is possible to construct an associated graded algebra connected with an algebraic algebra in such a way that the positive part is graded nil, i.e., all homogeneous elements are nil. On the other hand, the Kurosh Problem has a negative solution for rings with finite Gelfand-Kirillov dimension ( [30]), for simple rings ( [42]), for primitive rings ( [2]), for finitely generated primitive rings ( [8]), and for finitely generated algebraic primitive rings ( [9]). However, a natural question arising from the general Kurosh Problem remains open: Question 4 (Small's question).…”