All rings in this paper are commutative, and acc ⁡ ⊥ \operatorname {acc} \bot (resp., acc ⊕ \operatorname {acc} \, \oplus ) denotes the acc on annihilators (resp., on direct sums of ideals). Any subring of an acc ⁡ ⊥ \operatorname {acc} \bot ring, e.g., of a Noetherian ring, is an acc ⁡ ⊥ \operatorname {acc} \bot ring. Together, acc ⁡ ⊥ \operatorname {acc} \bot and acc ⊕ \operatorname {acc} \, \oplus constitute the requirement for a ring to be a Goldie ring. Moreover, a ring R R is Goldie iff its classical quotient ring Q Q is Goldie. A ring R R is a Kerr ring (the appellation is for J. Kerr, who in 1990 constructed the first Goldie rings not Kerr) iff the polynomial ring R [ x ] R[x] has acc ⁡ ⊥ \operatorname {acc} \bot (in which case R R must have acc ⁡ ⊥ \operatorname {acc} \bot ). By the Hilbert Basis theorem, if S S is a Noetherian ring, then so is S [ x ] S[x] ; hence, any subring R R of a Noetherian ring is Kerr. In this note, using results of Levitzki, Herstein, Small, and the author, we show that any Goldie ring R R such that Q = Q c ( R ) Q = {Q_c}(R) has nil Jacobson radical (equivalently, the nil radical of R R is an intersection of associated prime ideals) is Kerr in a very strong sense: Q Q is Artinian and, hence, Noetherian (Theorems 1.1 and 2.2). As a corollary we prove that any Goldie ring A A that is algebraic over a field k k is Artinian, and, hence, any order R R in A A is a Kerr ring (Theorem 2.5 and Corollary 2.6). The same is true of any algebra A A over a field k k of cardinality exceeding the dimension of A A (Corollary 2.7). Other Kerr rings are: reduced acc ⁡ ⊥ \operatorname {acc} \bot rings and valuation rings with acc ⁡ ⊥ \operatorname {acc} \bot (see 3.3 and 3.4).