Sets of Commuting Derivations and Simplicity

A ring R is simple under a set D of derivations if no nontrivial ideal of R is preserved by all derivations in D. Continuing previous joint work with C. J. Maxson, the author provides a computational test for the simplicity of k[x ₁,…,x _n ]/〈 x ₁ ^p ,…, x _n ^p 〉 (k a field of characteristic p > 0) under a set of commuting k-derivations. Specific rings are then examined for sets of commuting derivations, especially those under which the ring is simple. The possible sizes and minimality of such sets are also determined in particular cases.